Shape-shifting a configuration of reusable elements

ABSTRACT

An apparatus, an element for a game assembly, and a game assembly apparatus. The apparatus includes a three-dimensional body having a geometric shape and which is displaceable between an initial state and a goal state that is different from said initial state. A motion-restriction function is to limit the displacement of a centre point of the body with respect to a centre point of another body along a trajectory. At least one sensor is to provide input regarding the presence of another body in contact with the body and which is to allow the displacement of the body based on the input. A computer program is to allow displacement of the body based at least part of on a factor of randomness.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is a continuation of U.S. patent applicationSer. No. 14/052,435 (filed on Oct. 11, 2013), which is acontinuation-in-part of U.S. patent application Ser. No. 13/843,340(filed on Mar. 15, 2013), which are each hereby incorporated byreference in their entireties.

TECHNICAL FIELD

Embodiments relate to an assembly of elements, and elements suitable andconfigured for such an assembly.

BACKGROUND

Since the history of man, people are making constructions of all kinds.In order to make constructing easier, a construction was divided intoelements. These elements were standardized to make production easier.Examples of this standardisation are, for buildings for instance, bricksfor building a house, beams and roof tiles, and more recently concreteparts like floor panels, windows, but also doors and other parts of abuilding. This concept of standardized parts is also used for othertypes of constructions, like cars, computers, and, in fact, allindustrially produced constructions.

A problem with most of these elements is that they require handling.Furthermore, the elements are used for a specific construction, or aspecific use, like toys. Furthermore, often the known elements are notreusable.

In “Reconfigurable group robots adaptively transforming a mechanicalstructure”, by Yousuke Suzuki, Norio Inou, Hitishi Kimura, MichihikoKoseki, Proc. Of the 2006 IEEE/RSJ, Oct. 9-15, 2006, Beijing, China,“group robots adaptively construct a mechanical structure” aredescribed. “The feature of the robots is high rigidity by adoptingsliding mechanisms. [.] discussed algorithms of crawl motion andadaptive construction considering mechanical constraints of the robots.The proposed algorithm is based on local communication of the robots.[.]a scheme of a temporary leader which is autonomously specified byform of the structure. The scheme decreases amount of information incommunication between the robots.” A proposed motion module allows onlya limited mobility of the proposed robots.

SUMMARY

Embodiments relate to a system of elements that allow a flexible use.

Embodiments thus pertain to a system comprising at least a first, asecond and a third element, and a motion module, said elements beingthree-dimensional and each element comprising: a centre point in saidelement; at least one face coupled to said centre point and comprising:a motion-guiding module, defining a trajectory over at least part ofsaid face; a motion-restriction module, adapted for limiting thedisplacement of said centre point with respect to said centre point ofone of the other elements to at least one trajectory selected from thegroup consisting of said trajectory and said trajectory of said otherelement, when interacting with said motion module, wherein said motionmodule is adapted to be coupled to a face of one of said elements, andadapted for displacing said centre point of said one element withrespect to said centre point of one of the other elements wheninteracting with the motion-guiding module of said one of the otherelements, said motion-guiding module, said motion module and saidmotion-restriction module defining different module types, wherein fordisplacing said centre point of said first element away from said centrepoint of said second element and towards said centre point of said thirdelement, a first face of said at least one face of said first elementfaces at least one of a second face of said at least one face of saidsecond element and a third face of said at least one face of said thirdelement, thus providing facing faces, and wherein for said displacing:said motion module interacts with at least one motion-guiding module,and with at least one motion-restriction module, with said facing facesproviding said interacting modules while displacing; at least one moduleof said first face interacts with at least one module of at least onedifferent module type of at least one other of said facing faces whiledisplacing, and said at least one module of said first face interactswith at least one module of a different module type of said second faceand at least one module of a different module type of said third face.

It was found that such a system with the elements allow flexibleconstruction of an object. It may even be possible to design theelements within the current definition to group the elements into anobject and to change the shape of an object autonomously. In accordancewith embodiments, at least one element can be provided with a buildingplan for the shape. In an alternative embodiment, the building plan canbe distributed over elements, and by communicating and distributingcontrol, the elements together may accomplish shifting the shape. Abuilding plan may consist of a definition of the eventual shape of anobject. It may alternatively comprise intermediate constellations ofelements, or intermediate shapes to arrive to an end shape.

In this description, a configuration is used for an assembly of elementsthat are grouped together in a substantially consistent orientation withrespect to one another. The elements in such a configuration may form anobject. For such an object to change its shape, one or more elementsmove or displace with respect to other elements. This statement,however, does not work the other way around: Elements may havedisplaced, but that does not always mean that the shape of the objectchanged. If at least some of the elements of an object displace in apredefined manner, it is possible to in fact have displaced the entireobject.

In accordance with embodiments, faces of elements face other faces. Inits broadest sense, faces are thus directed to one another. The facingfaces may be opposite one another. In accordance with embodiments,facing faces may at least partly overlap.

In accordance with embodiments, faces may be curved. In accordance withembodiments, faces are flat, planar. Thus, a face defines a plane overwhich In accordance with embodiments a face of another element canslide. In such a state, faces are facing, and during said slidingopposite one another and partly overlapping.

The various modules and parts are ‘coupled.’ In particular, this relatesto functionally coupled. In particular embodiments, this relates toparts or modules that are physically coupled. More in particular, Inaccordance with embodiments it is used to cover connected. Specifically,In accordance with embodiments parts, faces, modules and the like thatare fixed or mounted. In this respect, fixed refers to for instancewelding, gluing, and the like. Mounted may refer to the use ofattachment provisions, like bolts and nuts.

“Interacting” relates to modules and/or elements that exert force to oneanother, but also to exchanging data, exchanging instruction programparts, and exchanging feedback. In accordance with embodiments,interacting relates to modules and/or elements that are in contact. Inaccordance with embodiments, interacting relates to modules and/orelements that are engaging.

Various modules are provided “for displacing.” This relates functionallyto the process of displacing an element. It can also includepreparations for displacing elements. “For displacement” may alsoinclude post-processing. It may include, for instance, displacement ofone or more motion modules over one or more faces of an element, orbetween elements, to their actual position on a face where they startdisplacing an element. It may for instance also include storing a motionmodule after use, or transmission of an end position to other elements.“For displacing” may for instance also include the time during whichdata is exchanged in preparation for setting an element in motion.

“While displacing” refers to the time frame during which elements areactually in motion. For displacing elements, multiple instances of“while displacing” may occur.

The faces are provided to allow a face to exert or transmit a force toanother face.

A movement of an element can in fact be split into an actualdisplacement of a centre point of an element, and a change inorientation. A change of orientation is for instance a rotation about aline through the centre point: the centre point does not change itsposition. In this respect, the motion module of an element isinstrumental for an actual displacement of a centre point of an element.An element may further comprise an orientation module for changing theorientation of an element. In accordance with embodiments, the motionmodule and the orientation module may be combined.

An element may comprise parts defining an outer contour of an element.For instance, an element may comprise ribs. An element comprises a face.A face at least has supports allowing one element to rest on anotherelement. Ribs for instance define such a face. The space between ribsmay be open. Alternatively, support may be provided by exerting a force,for instance aerodynamic or electromagnetic forces. In accordance withembodiments, each element further comprising a face provided with asurface at a surface-distance from said centre point. Such a surfaceprovides a solid, physical support. A surface may be completely closed.Alternatively, a face may comprise a surface that has openings. Forinstance, the surface may be meshed. Often, such a face is planar,defining a bounded plane.

In a sense, the motion module in fact drives the movement of an elementwith respect to another element.

The motion-guiding module in a sense steers a direction of displacementof an element with respect to another element. In a case when oneelement is in contact with another element, the motion guiding modulemay comprise a track on one element and the other element follows thattrack.

One or more of the elements may further comprise a motion-restrictionmodule adapted for limiting the displacement of said centre point withrespect to said centre point of one of the other elements to at leastone trajectory selected from the group consisting of said trajectory andsaid trajectory of said other element, when interacting with the motionmodule of the other element. The interaction between at least one of themotion module, the motion-guiding module and the motion-restrictionmodule from the face of an element with at least one different modulefrom an element with a facing face may in fact restrict the distancebetween those elements. It may hold these elements together or releasethese elements to allow them to move away from one another. It may alsokeep the distance between these elements between defined limits. Incombination and/or in a separate action, the interaction may also keeporientation of these element with respect to one another elementslimits. This function occurs while a motion module, a motion-restrictionmodule and a motion-guiding module interact. This may also be the casewhen elements are not displacing any more. In such a case, modules maystill be interacting. This may be referred to as a holding state.

The modules of the current system, in particular, the elements, providea reliable displacement of elements. The result of a displacement is atleast partially predictable. Displacement follows at least part of atrajectory. Interaction between on or more motion modules, one or moremotion guiding modules, and one or more motion restriction modules limitthe displacement of a centre point with respect to one or more othercentre points of other elements to at least one trajectory. Such atrajectory may be predefined. It may be a fixed route over a face. Forinstance, a rail provides such a fixed route.

In accordance with embodiments, a system comprises at least a first, asecond and a third three-dimensional element, each element comprising: acentre point in said element; a motion-guiding module, coupled to saidcentre point and defining a trajectory over said element; a motionmodule, adapted for displacing the centre point with respect to a secondcentre point of one of the other elements using the motion-guidingmodule of that other element; a motion-restriction module, adapted forlimiting the displacement of said centre point with respect to saidsecond centre point to at least one trajectory selected from the groupconsisting of said trajectory and a second trajectory of said otherelement, wherein said motion-guiding modules of at least two of saidelements are functionally coupled for enabling said motion module todisplace the centre point of a third displacing element which is incontact with one of the other two elements away from the centre point ofone of the other two elements and towards the centre point and incontact with the other of the other two elements.

In accordance with embodiments, said first face changes its interactingmodule for said displacing.

In accordance with embodiments, while displacing, said motion module iscoupled to said first face.

In accordance with embodiments, at least one module of said second faceand at least one module of said third face interact with a differentmodule of said first face while displacing.

In accordance with embodiments, said modules of said second face andsaid third face interact one after the other.

In accordance with embodiments, said modules of said second face andsaid third face interact one after the other with a different module ofsaid first face for said displacing.

In accordance with embodiments, said modules of said first, second andthird face interact alternatingly while displacing.

In accordance with embodiments, for said displacing, at least one ofsaid modules from each of said first, second and third face interacts.

In accordance with embodiments, each of said elements comprise a motionmodule. In particular, each of the elements comprises at least onemotion module. This increases flexibility and speed.

In accordance with embodiments, each of said at least one face of saidelements comprises a motion module. This again increases speed andflexibility, allowing elements to work for instance autonomously, or insubgroups.

In accordance with embodiments, each element comprises at least two ofsaid faces. With proper orientation of faces of an element with respectto one another, for instance motion in two dimensions and eve threedimensions becomes easier to accomplish.

In accordance with embodiments, said motion module is adapted forchanging an orientation of said one element, coupled to said motionmodule, and an other element, having a face having a module interactingwith said motion module, with respect to one another, in particularrotating said face coupled to said motion module and a face facing saidface coupled to said motion module with respect to one another, more inparticular rotating about an axis through said centre point of said oneelement.

In accordance with embodiments, at least one of said elements furthercomprises an orientation module, adapted for changing an orientation ofsaid one element and another of said elements with respect to oneanother, in particular, rotating said face coupled to said orientationmodule and a face facing said face coupled to said orientation modulewith respect to one another, more in particular rotating about an axisthrough said centre point of said one element.

In accordance with embodiments, said motion module is adapted fordecoupling from said face.

In accordance with embodiments, said motion module is displaceable whenit is decoupled from said face.

In accordance with embodiments, said motion module is displaceable to aneighbouring element when it is decoupled from said face.

In accordance with embodiments, said one element comprises at least twofaces, and said motion module is displaceable from one face to a nextface of said one element.

In accordance with embodiments, said motion module is displaceableinside said element from one face to another face of said one elementwhen it is decoupled from said face.

In accordance with embodiments, said motion module, said motionrestriction module and said motion guiding module comprise a holdingstate in which at least partially overlapping facing faces are held intheir mutual position, said holding state, in particular, involving atleast a motion module from one face and a motion restriction module froma face facing said one face.

In accordance with embodiments, each element comprises a holding module,coupled to a face, for interacting with a holding module of a facingface for holding said face positioned with respect to said facing face.The holding module hold at least one from position and orientation. Inaccordance with embodiments, the holding module of an element may engageanother element. In accordance with embodiments, said holding modulecomprises two parts, adapted to exert a force to one another for holdingelements positioned and/or in their orientation with respect to oneanother. In accordance with embodiments, one element actuates its firstholding module part to engage the second holding module part of anotherelement. In this or another embodiment, the other element may in turnactuate its second holding module part to disengage from the firstholding module part of the other element.

In accordance with embodiments, said holding module comprises two parts,adapted to exert a force to one another for holding faces positioned.

In accordance with embodiments, said holding module comprises two parts,adapted to exert a force to one another for holding faces positioned,and wherein said two parts are provided to faces comprising said holdingmodule, allowing each face provided with said holding module to be heldin position with respect to a facing face provided with said holdingmodule, with the one holding module part of a face interacting withanother holding part of a facing face.

In accordance with embodiments, said holding module comprises a holdingstate in which the holding module holds faces positioned, and a releasedstate in which faces can move with respect to one another.

In accordance with embodiments, said at least one face of said eachelement is connected to said element.

In accordance with embodiments, said motion module is connected to saidface.

In accordance with embodiments, the system further comprises a fourthsuch element comprising at least the features of the first, second andthird elements, and providing a fourth of said at least one face to saidsystem.

In accordance with embodiments, for said displacing, said fourth facefaces said first face.

In accordance with embodiments, during said displacing said firstelement displaces in a first direction, and wherein a further,subsequent, displacing comprises: at least one module of said first faceinteracts with at least one module of at least one different module typeof said fourth face while further displacing in a further directiondifferent from said first direction, in particular at an angle to saidfirst direction.

In accordance with embodiments, said first element further comprises afurther at least one of said faces, providing a fifth face to saidsystem. For displacing said fifth face may face said fourth face.

In accordance with embodiments, during said displacing said firstelement displaces in a first direction, and wherein a further,subsequent, displacing comprises: said fifth face facing said fourthface, and at least one module of said fifth face interacts with at leastone module of at least one different module type of said fourth faceswhile further displacing in a further direction different from saidfirst direction during said displacing.

In accordance with embodiments, the motion-guiding module of at leastone of said elements is adapted for providing said trajectoryfunctionally around said element.

In accordance with embodiments, said motion-guiding module of said atleast one element is adapted for defining a further, second trajectorycrossing said predefined, first trajectory. This allows in operationdisplacement of one of the other elements in two dimensions.

In accordance with embodiments, said elements comprising at least two ofsaid faces, provided with a surface at a surface-distance from saidcentre point.

In accordance with embodiments, at least part of said motion module isadapted for displacing internally inside said element.

In accordance with embodiments, at least part of said motion module isadapted for changing its orientation inside said element.

In accordance with embodiments, said elements comprise at least two ofsaid faces, said elements neighbouring one another and saidmotion-guiding modules of said faces connected to one another.

In accordance with embodiments, said faces comprise boundaries, withsaid motion-guiding modules running to at least one of said boundaries.

In accordance with embodiments, said motion-guiding module comprises atrail of detectable indications, in particular, a trail ofelectromagnetic radiation, like light, a magnetic trail, anelectrostatic trail, sound or ultrasound trail. When provided with oneor more sensors, the trail can be followed.

In accordance with embodiments, said trajectory comprises a physicaltrack.

In accordance with embodiments, said trajectory comprises a rail. Anexample of this is for instance a type of rails that a train uses.

In accordance with embodiments, said trajectory at least partly followsa straight line.

In accordance with embodiments, said element comprises at least one facecomprising a surface provided with said motion-guiding module.

In accordance with embodiments, said motion-guiding module comprises atleast two motion-guiding parts defining a plane.

In accordance with embodiments, two motion-guiding parts have at leastone crossing, in particular, said motion-guiding parts are straight andcross one another rectangularly.

In accordance with embodiments, said element comprises at least one facecomprising a surface provided with said motion module, in particular,said surface is a flat plane forming a face of said element.

In accordance with embodiments, said element comprises at least one facecomprising a surface provided with said motion module and saidmotion-guiding module.

In accordance with embodiments, said element comprises a series of faceseach having a surface, in particular, said faces defining said element.

In accordance with embodiments, said element comprises a series of atleast two of said faces, in particular, said element comprises a seriesof coupled faces forming faces of said element.

In accordance with embodiments, said element comprises at least fourfaces, in particular at least 6 faces, more in particular, opposite andhaving a normal direction orthogonal normal.

In accordance with embodiments, said element is a regular body.

In accordance with embodiments, said element is substantially a block,more in particular, a cube. An advantage of cubes is that they alloweasy stacking.

In accordance with embodiments, said motion-restriction module comprisesa first motion-restriction module part, arranged for physically engaginganother element, and restricting motion in a first direction having acomponent perpendicular to said trajectory.

In accordance with embodiments, said motion-restriction module comprisesa second motion-restriction module part, arranged for physicallyengaging another element and restricting motion in a second directionhaving a component perpendicular to said trajectory and perpendicular tosaid first direction.

In accordance with embodiments, an element comprises: at least one facecomprising an exterior surface for providing abutment for a face ofanother, similar element; at least one holding module for holding saidelement with respect to at least one other, similar element, saidholding selected from holding position and holding orientation; at leastone motion module for moving said element with respect to at least oneother, similar element substantially along or on an exterior surface ofat least one other, similar element, said moving selected fromdisplacing of a centre of mass with respect to one another, displacing ageometrical centre with respect to one another, and changing anorientation with respect to one another; a communication module forexchanging data with at least one other, similar element, said datacomprising at least one position status; a data processing module,functionally coupled to said communication module for processing datafrom said communication module; an energy module functionally coupledfor providing energy to at least said displacement module, saidcommunication module, and said data processing module, wherein said dataprocessing module comprises software which, when running on said dataprocessing module, comprises: retrieving a set position, selected fromplace and orientation and a combination thereof, for said element viasaid data communication module; retrieving current position information;producing at least one motion instruction for said motion module formoving said element from said current position to said set position bymoving its exterior surface over or along said exterior surface of saidat last one other, similar element; providing said motion module withsaid at least one motion instruction.

In this respect, producing a motion instruction may comprise calculatinga motion instruction, or it may comprise calculating intermediate steps.Thus, it may comprise calculating at least one motion instruction formoving said element towards said set position.

In accordance with embodiments, in operation said element is in physicalcontact with at least one other, similar element with its exteriorsurface at least partly in contact with at least part of an exteriorsurface of said at least one other, similar element.

In accordance with embodiments, elements comprise at least one exteriorsurface and when displacing, the surface displaces substantiallyparallel to an abutting exterior surface of another, similar element. Inaccordance with embodiments, the surfaces slide with respect to oneanother, with for instance an air cushion between the surfaces, or witha small distance for instance using magnetic levitation. An element canthus “hover” over another element.

An element can be characterised by its position and orientation. Bothposition and orientation may be absolute and relative. The relativeposition can be defined as a position of an element with respect to oneor more other elements. Relative position may also be defined as theposition of an element in an object it forms together with otherelements, or the position in a group of elements. In accordance withembodiments, elements may be provided with a position sensing partfunctionally coupled to said data processing module.

In accordance with embodiments said position sensing part comprises arelative position sensing part for sensing the position of said elementwith respect to at least one other, similar element. Such an element maybe in contact with said element.

In accordance with embodiments said position sensing part comprises alocal absolute position sensing part for sensing the local position ofsaid element with respect to a location within a group of elements.

In accordance with embodiments said position sensing part comprises anabsolute position sensing part for sensing the global position of saidelement.

In accordance with embodiments an element comprises anorientation-sensing part functionally coupled to data processing module.

In accordance with embodiments, said orientation-sensing part comprisesa relative orientation sensing part for sensing the orientation of saidelement with respect to at least one other, similar element which is incontact with said element.

In accordance with embodiments said orientation-sensing part is adaptedfor sensing the orientation of said element with respect to a forcefield, for instance a gravitational force field, an electrostatic forcefield, a magnetic force field.

In accordance with embodiments said motion module comprises a rail withdisplacer. In order to actually displace an element with respect toanother element, a displacer of one element runs in or on a rail ofanother element. The displacer may physically engage the rail.Alternatively, it may exert one or more forces to the rail, even withoutbeing in physical contact with the rail, like for instance exertingmagnetic forces.

In accordance with embodiments said rails runs in at least twodimensions, in particular, on/in exterior surface.

In accordance with embodiments, elements may comprise a shareddisplacer.

In accordance with embodiments said motion module comprises at least onepiezo element (“stepper”).

In accordance with embodiments said element comprises walls defining theouter boundaries of an element.

In accordance with embodiments, at least one exterior wall may beprovided with a seal for sealing space between surfaces of elements.Thus, it is possible, using elements, to build a leak-tight, or even anair-tight construction.

In accordance with embodiments said seal has an engaging position anddisengaging position.

In accordance with embodiments said seal is circumferential orperipheral with respect to a wall of an element. The seal may compriseparts that run along sides of a wall.

In accordance with embodiments, at least one wall comprises a planarsurface part.

In accordance with embodiments, an element comprises at least onefunctional surface, for instance comprising a photovoltaic element.Alternatively or in combination, a functional surface is provided withone or more display elements. A display element may comprise one or morepixels that may form a display. In accordance with embodiments, theneighbouring surfaces of several elements may form a display. Thus, theelements allow presentation of visual information. Furthermore oralternatively, the functional surface may comprise touch-functionalityand/or proximity-sensing, allowing formation of for instance a touchpanel. In accordance with embodiments, elements can be combined to forma display for playing movies, television, or games. In case of elementswhich have sides smaller than 1 cm, the elements will in many instancescombine the functional surfaces into one display of combinedelement-functional surfaces.

In accordance with embodiments, said element comprises a container spacein said element, in particular, a closable container space.

In accordance with embodiments said container space comprises a closureor an actuator for closing said container. In accordance withembodiments said actuator is functionally coupled to said dataprocessing module.

In accordance with embodiments, said element comprises at least oneactuator for selectably operating said motion module, in accordance withembodiments, for retracting said motion module within said element. Inaccordance with embodiments, said actuator is functionally coupled tosaid data processing module.

In accordance with embodiments, said data processing module may compriseany one selected from: a memory, a master-slave setting, a dynamicmaster slave setting, a building plan, time-based position instructions,a time keeping part.

In accordance with embodiments, the size of the elements is 10 cm downto 0.1 micron, in particular 1 cm down to 0.5 micron, more in particular1 mm down to 0.5 micron, specifically 100 micron down to 0.1 micron.

Embodiments further relate to a method for conveying material,comprising providing said material in at least one element describedabove.

Embodiments further relate to an element comprising: at least oneexterior surface, for instance a wall, allowing displacement; at leastone holding module, for maintaining a position of said element withrespect to or onto a similar element; and at least one motion module fordisplacing said element with respect to other, similar elementssubstantially over said exterior surface; the motion module can also bea separate part shared with at least one other element, see rail forexample, or it can induce linear displacement, rotation, displacing ofcentre of mass with respect to one another, change of orientation withrespect to one another; changing distance of said element with respectto other, similar elements; Furthermore, a telescope part may beprovided on the element.

In accordance with embodiments, the element may further comprise: acommunication module for exchanging data with other, similar elements;in particular, said data comprising orientation, position with respectto others, fixation, external physical parameters like temperature,sensor data, time, or software or firmware updates, said communicationmodule may be adapted for wireless transmission of data.

In accordance with embodiments, the element may further comprise: a dataprocessing module.

In accordance with embodiments, the element may further comprise: anenergy module, for instance for providing energy to said motion module,motion-restriction module, to said communication module, to said dataprocessing module, for instance providing said energy usingelectromagnetic radiation, wireless transfer, energy from other, similarelement, the energy module may also provide storage or energy.

In this respect, “similar” refers to elements comprising at least oneface provided with a holding module and a motion module that allowscooperation.

In accordance with embodiments, said elements are in physical contactwith one another; in particular, at least parts of said walls orexternal surfaces are in physical contact with one another. Inparticular, an area of contact is defined; motion module in contact,holding modules in contact; forces pressing one construction elementonto another can be taken up via displacement module, holding module, atleast part of said exterior surface.

In accordance with embodiments, elements may be combined in an object,where their position may be defined with respect to the object or withrespect to other elements. In this respect, the neighbourhood may be ofimportance. In accordance with embodiments, the neighbourhood is definedas one beyond said element. In accordance with embodiments, theneighbourhood may be two elements beyond said element.

In accordance with embodiments, an element is at least partly producedusing for instance 3D printing. In accordance with embodiments, plantcells may be used for producing a “wood” surface. Such plant cells maybe attached to a carrier substrate.

In accordance with embodiments, elements in an assembly of elements worktogether, wherein said elements have a master/slave setting, inparticular, a dynamic master/slave setting.

Embodiments further relate to a game assembly, comprising a systemdescribed above, and a computing device in communication with at leastone of said elements, said computing device running a computer programwhich, when operating on said computing device, performs: requesting auser input for defining a start configuration of said elements;requesting a user input for defining an end configuration of saidelements; communicating said start configuration and said endconfiguration to at least one of said elements.

Embodiments also relate to a computer implemented construction tool,comprising a computer program which, when running on a computer device,performs: defining in a memory a set of at least three elements, eachelement comprising: a centre point in said element, a relative positionand an orientation; a motion-guiding function, coupled to said centrepoint and defining a trajectory over said element; a motion functiondefining displacing the centre point with respect to a second centrepoint of one of the other elements using the motion-guiding function ofthat other element; a motion-restriction function, adapted for limitingthe displacement of said centre point with respect to the second centrepoint to at least one trajectory selected from the group consisting ofsaid trajectory and a second predefined trajectory of said otherelement, wherein said motion-guiding function of at least two of saidelements define a functionally coupling between elements for enablingsaid motion function to displace the centre point of a third, displacingelement which is in contact with one of the other two elements away fromthe centre point of one of the other two elements and towards the centrepoint and in contact with the other of the other two elements.

In this respect, the construction tool may also be seen as a game, agame, or a simulation, in which features of functional elements aremodified and effects of modification may be explored. Other functionsmay for instance be: sensing other elements; defining in a memory astart configuration of said elements; defining in a memory an endconfiguration of said elements.

Embodiments further relate to a method for playing a game, comprisingproviding a computer program which, when running on a computer device,performs: defining a set of at least three three-dimensional elements ina memory, each element having a centre point and at least one face;defining in a memory a start state of said set of elements, by a startouter boundary of said set of elements, and a at least a position ofeach element with respect to said outer boundary; defining in a memoryan goal state of said set of elements, which goal state is differentfrom said start state and requiring displacement of at least oneelement; providing a function toolbox comprising: a set ofmotion-guiding functions, said motion-guiding functions coupled to saidcentre point and defining a trajectory over said element; a set ofmotion functions defining displacing the centre point with respect to asecond centre point of one of the other elements using themotion-guiding function of that other element; a set ofmotion-restriction functions, adapted for limiting the displacement ofsaid centre point with respect to said second centre point to at leastone trajectory selected from the group consisting of said trajectory anda second trajectory of said other element; a set of sensor functionsproviding information on the environment of an element; presenting saidfunction toolbox to a user and enabling said user to select at least onefunction from said function toolbox for each element; providing for eachelement an element computer program operationally coupling said selectedfunctions, and which element computer program when executed collectssensor input, relative position input, and allows motion; running oneach element said element computer program.

Again, a game may also be or comprise a simulation as explained above.

In particular, the method comprises providing input regarding thepresence of another element in contact with at least one face.

In accordance with embodiments, said method further comprises definingin a memory a goal state of said set of elements by an end outerboundary of said set of elements.

In accordance with embodiments, said method further comprises definingin a memory a goal state of said set of elements by defining for atleast one element a requirement with respect to said set of elements.

In accordance with embodiments, said method further comprises definingin a memory a goal state of said set of elements by defining for atleast one element a requirement with respect to at least one element ofsaid set of elements.

In accordance with embodiments, said method further comprises definingin a memory a goal state of said set of elements by defining for atleast one element a requirement with respect to at least one specificelement of said set of elements.

The behaviour of an element in accordance with embodiments has a factorof randomness. For instance, a selection of a direction of motion maycomprise a factor of randomness. In accordance with embodiments, themotion of an element may be based upon a genetic algorithm. In anexample, a random generator influences the selection of for instance thedirection of motion. In case such a random selection has a good effect,for instance it brings an element closer to a final goal, a value of aweight factor associated with the direction is increased. If the randomselection has a bad effect, the value of the weight factor is decreased.

In a broader sense, the behaviour of an element may at least partly becontrolled, or problems that an element or an assembly or system ofelements face may be solved, using an evolutionary algorithm. An elementin this embodiment comprises a controller comprising machineinstructions using an evolutionary algorithm. An evolutionary algorithmgenerates solutions to optimization problems using techniques inspiredby natural evolution. A genetic algorithm in fact is a type of anevolutionary algorithm. Further examples of evolutionary algorithms areinheritance, mutation, selection, and crossover. An evolutionaryalgorithm uses for instance mechanisms inspired by biological evolution,such as reproduction, mutation, recombination, and selection. Many ofthese algorithms and mechanisms have a factor of randomness or chance: Aproperty or a choice that needs to be made can at least partly be basedupon a random selection. In this way, solutions and operational modesmay be found that provide a better solution to a problem.

Due to changes in the environment of elements and/or a vast amount ofoptions, an exact solution or even an optimal solution, and/or forinstance a statistical probability that a solution may reach an endgoal, may not always be calculated within an available time frame. Whenfor instance one element changes its position, a calculation at/ofanother element may become invalid.

Similar techniques, similar to evolutionary algorithms, differ in theimplementation details and the nature of the particular applied problem.As such, these techniques are known in the art of computer softwaredevelopment. An element, at least part of the elements, or an assemblyof elements may use the following algorithms or combinations thereof:

Genetic algorithm: Elements may use it for solving a problem, forinstance in the form of strings of numbers (traditionally binary,although the best representations are usually those that reflectsomething about the problem being solved), by applying operators such asrecombination and mutation (sometimes one, sometimes both).

Genetic programming: Elements may use it for making their controlinstructions more flexible. Effectiveness of for instance parts ofcomputer programs in solving a problem is evaluated, and their fitnessis determined by their ability to solve a (computational) problem.

Evolutionary programming: Usually, the structure of a computer programis fixed and its numerical parameters are allowed to evolve.

Gene expression programming:—Like genetic programming, GEP also evolvescomputer programs but it explores a genotype-phenotype system, wherecomputer programs of different sizes are encoded in linear chromosomesof fixed length.

Evolution strategy—Works with vectors of real numbers as representationsof solutions, and typically uses self-adaptive mutation rates.

Memetic algorithm—It is the hybrid form of population based methods.Inspired by the both Darwinian principles of natural evolution andDawkins' notion of a meme and viewed as a form of population-basedalgorithm coupled with individual learning procedures capable ofperforming local refinements.

Differential evolution—Based on vector differences. Elements may use itfor solving numerical optimization problems.

Neuro-evolution—Similar to genetic programming but the genomes representartificial neural networks by describing structure and connectionweights. The genome encoding can be direct or indirect.

Learning classifier system is a machine learning system with close linksto reinforcement learning and genetic algorithms. It for instancecomprises a population of binary rules on which a genetic algorithmaltered and selected the best rules. Rule fitness may be based on areinforcement learning technique.

The elements or assembly of element may also use so called Swarmalgorithms, including:

Ant colony optimization—Based on the ideas of ant foraging by pheromonecommunication to form paths. Elements may use this when confronted withcombinatorial optimization and graph problems.

Bees algorithm is based on the foraging behaviour of honey bees. Whenelements face problems like routing and scheduling.

Cuckoo search is inspired by the brooding parasitism of the cuckoospecies. It also uses Levy flights. Elements may use the algorithmglobal optimization problems.

Particle swarm optimization—Based on the ideas of animal flockingbehaviour. Elements may use this algorithm for numerical optimizationproblems.

Other population-based meta-heuristic methods comprise:

“Firefly algorithm,” inspired by the behaviour of fireflies, attractingeach other by flashing light. This is especially useful for multimodaloptimization.

Harmony search—Based on the ideas of musicians' behaviour in searchingfor better harmonies. This algorithm is suitable for combinatorialoptimization as well as parameter optimization.

Gaussian adaptation—Based on information theory. Used for maximizationof manufacturing yield, mean fitness or average information. See forinstance Entropy in thermodynamics and information theory.

It was found that a deterministic set of instructions defining for anelement its actions does not always work: Sometimes, due to changes ofand in the environment and the number of options that are possible, a‘best solution’ of actions to achieve a goal does not exist, or may taketoo long to calculate. For instance, calculations in one element maybecome invalid when another element changes its position or orientation.Alternatively, one or more subsets of actions may be defined toaccomplish intermediate goals.

Embodiments further relate to a system comprising at least a first, asecond and a third three-dimensional element, each element comprising: acentre point in said element; a motion-guiding module, coupled to saidcentre point and defining a trajectory over said element; amotion-restriction module, adapted for limiting the displacement of saidcentre point with respect to the second centre point to at least onetrajectory selected from the group consisting of said trajectory and asecond trajectory of said other element; a motion module, adapted fordisplacing the centre point of an element with respect to a secondcentre point of one of the other elements, said motion module adaptedfor engaging the motion-guiding module of at least one of the element,wherein said motion-guiding modules of at least two of said elements arefunctionally coupled for enabling said motion module to displace thecentre point of a third, displacing element which is in contact with oneof the other two elements away from the centre point of one of the othertwo elements and towards the centre point and in contact with the otherof the other two elements.

In accordance with embodiments, said motion module, also referred to asa shared motion module, can move along an element from one face toanother. At a face, or a position on a face, the shared motion modulecan functionally perform its function of motion module. When movingalong an element from one face to another, the centre point of anelement may remain at rest. In accordance with embodiments, the sharedmotion module can even travel from one element to a next element, inparticular, a neighbouring element.

The shared motion module in accordance with embodiments engages themotion guiding module. It thus uses provisions in or on an element thatare already present. If, for instance, the elements are provided withtracks, motion guiding module engagement parts of the shared motionmodule may engage the motion guiding module. Such a motion guidingmodule may for instance be provided below the surface of a face of theelement, like for instance a flush-mounted track. This allows a sharedmotion module to displace below the surface of a face of an element.

In order to be able to displace one element with respect to at least oneother element, the shared motion module may comprise a releasableattachment part for attaching the shared motion module to an element.Releasing the attachment part allows the shared motion module todisplace with respect to an element, and activating the attachment partkeeps the shared motion module attached to an element. The attachmentpart of the shared motion module may engage an element, for instance byexerting a force, like a magnetic force. Alternatively, the attachmentpart may physically engage the element. A mechanical attachment part cancooperate with cooperating attachment parts provided in the element. Forinstance, the shared motion module may comprise an anchoring pin lockinginto an anchoring hole in an element, or vice-versa, the shared motionmodule can be provided with the anchoring hole.

In order to be able to displace an element, the shared motion module maycomprise an element displacement part. Such an element displacement partengages a motion guiding module on another element. Often, the otherelement is an element which is in face contact with an element that(temporarily) houses the shared motion module. The element displacementpart exerts a displacing force on a motion guiding module of anotherelement. This can be a mechanical force, for instance from a wheelrunning in a track, a gear wheel running on a rack rail, orpiezoelectric elements exerting force. Alternatively, for instance amagnetic force may be exerted. Often, the element displacement partextends from a face of an element that is engaged by the shared motionmodule.

In order to displace along an element, or even move from one element toanother, the shared motion module comprises a motion module movementpart. This motion module movement part may engage the motion guidingmodule of the element over of in which the shared motion module isdisplacing. In accordance with embodiments, the motion module movementpart is the element displacement part that is withdrawn to work on theelement that employs the shared motion module, or on or within theshared motion module travels. For instance, one or more wheels mayextend from the shared motion module in a direction facing away from theelement, thus enabling engagement of a neighbouring element. Thesewheels may be retracted to extend from the shared motion module at anopposite end, allowing engagement of the element using the shared motionmodule.

An element may comprise one or more storage provisions for storing ashared motion module.

A shared motion module may comprise one or more of the functional partsof an element that are mentioned in this description. A shared motionmodule may also comprise at least part of one or more of the functionalparts of an elements that are mentioned in this description. Forinstance, a shared motion module may comprise one or more selected formthe group consisting of a data processing device, data storage, anenergy storage device, energy generating device, a data communicationdevice, and a combination thereof. These devices and or functionalitiesare already described in relation to an element. This may even allowrelatively simple elements only having passive functional parts andshared motion modules having active parts for engaging an element. Inaccordance with embodiments, an element may comprise at least one motionmodule that can displace from a functional position at one face to afunctional position at another face of an element, Thus, an element maybe provided with one or more motion modules, reducing complexity of anelement. This no longer requires at least one motion module for eachface of an element.

In the current document, reference is made to three dimensional objectsor 3D objects. The elements are three dimensional. Thus, simply placingelements together on a plane surface already makes an object threedimensional. A three-dimensional object according to the currentdescription, however, refers to an object that is composed of coupledelements and extending at least two elements in each dimensionaldirection. Such a three-dimensional object or 3D object would have atleast 4 elements. In fact, three elements might already form a 3D objectwhen one or more elements are out-of-plane with respect to the otherelements.

In general, elements may comprise one or more faces that may be definedas being “polar.” Suppose that one type of face may be defined as havingthe property “plus” and another type of face may have the property“minus” with respect to at least one of the motion module, motionrestriction module, motion guiding module. Now suppose that a plus facecan only couple to and displace over a minus face. When using elementslike that, in general ordering of elements with respect to one anotherbecomes important when composing or building an object out of elements.In general formulation, an element comprises at least one face thatcomprises at least one mirror symmetry with respect to at least one faceof another element in view of at least one selected from the motionmodule, motion guiding module and motion restriction module when facingthat other face. These symmetries may be referred to as inter-facesymmetry. In accordance with embodiments, the at least one facecomprises at least one mirror symmetry with respect to the at least oneother face with respect to its shape. Thus, two elements have at leastone orientation with respect to one another in which they have arespective face and in which these faces fit on one another, can attachto one another, and move or displace over each others surface. In orderto provide flexibility to build an object from elements, in accordancewith embodiments an element comprises at least two non-polar faces. Inaccordance with embodiments, an element comprises less than four polarfaces. In particular, an element comprises less than three polar faces.Specifically, the polar faces are not provided on opposite sides of anelement.

On the other hand, elements may comprise one or more faces that havemirror symmetry regarding motion modules, motion restriction modulesand/or motion guiding modules in one or more mirror planes normal to theface or faces. Thus, an degree of intra-face symmetry may be provided.When using such elements, for elements to couple such faces or todisplace over such faces only requires proper rotational orientationwith respect to a rotational axis normal to those faces. When there ismirror symmetry in two perpendicular mirror planes, then couplingbecomes even easier. When the respective faces are for instance squareand these two mirror planes run through the centre of the square, thentwo square faces always couple exactly on top of one another. Thus, anincreasing symmetry of a face with respect to its motion module and/orits motion restriction module and/or its motion guiding module reducesthe need to check rotational orientation of elements with respect to oneanother. This again increases flexibility when building an object fromelements.

In accordance with embodiments, at least one face of an element hasmirror symmetry in a mirror plane normal to the face and through thecentre of the face. In particular, the face has mirror symmetry in twomirror planes that are normal to one another and the face. In accordancewith embodiments, the symmetry of the shape of the face and the symmetryof at least one of the motion module, the motion guiding module and themotion restriction module coincide.

Embodiments further relate to a game comprising shape-shifting an objectof elements from a first shape to a second shape, wherein the positionof at least one element with respect to at least one other of saidelements changes during said shape-shifting.

The elements can in fact form construction elements for assembling aphysical structure, for instance a building, a home, or the like. Tothat end, one or more symmetries of the shape of an element simplifiesconstruction of an object of elements.

The most familiar type of symmetry is geometrical symmetry. A geometricobject is said to be symmetric if, after it has been geometricallytransformed, it retains some property of the original object.

The most common group of transforms is the Euclidean group ofisometries, or distance-preserving transformations, in two dimensional(plane geometry) or three dimensional (solid geometry) Euclidean space.These isometries consist of reflections, rotations, translations andcombinations of these basic operations. Under an isometrictransformation, a geometric object is symmetric if the transformedobject is congruent to the original. For the elements to easily producean object, in accordance with embodiments the elements is symmetricunder at least one isometric transformation.

In accordance with embodiments, the elements have a shape to allowtessellation in at least two dimensions. More formally, a tessellationor tiling is a partition of the Euclidean plane into a countable numberof closed sets called tiles, such that the tiles intersect only on theirboundaries. These tiles may be polygons or any other shapes. Manytessellations are formed from a finite number of prototiles; all tilesin the tessellation are congruent to one of the given prototiles. If ageometric shape can be used as a prototile to create a tessellation, theshape is said to tessellate or to tile the plane, or, using elements, aspace. Certain polyhedra can be stacked in a regular crystal pattern tofill (or tile) three-dimensional space, including the cube (the onlyregular polyhedron to do so); the rhombic dodecahedron; and thetruncated octahedron.

To make stacking and formation of a three-dimensional object possiblewithout the need to control orientation of an element, the elements havean identical shape, and have a shape that allows filling a space. In twodimensions, tiling refers to filling a plane with identical Figures or aset of Figures. In the current discussion, elements arethree-dimensional and In accordance with embodiments have a shapeallowing substantially seamlessly filling a space. This is also referredto as tessellation. In a simple example, identical cubes easily fill aspace. In general, for instance polyhedra can be provided that allowfilling a space. As such, in mathematics, such shapes are known. Aspace-filling polyhedron, sometimes called a plesiohedron (Grünbaum andShephard 1980), is a polyhedron which can be used to generate atessellation of space. Tessellations in three dimensions are alsoreferred to as honeycombs.

Some literature state that the cube is the only Platonic solidpossessing this property (e.g., Gardner 1984, pp. 183-184). There are,however, other identical shapes that allows tessellation. One can simplyprove this by cutting a cube in regular pieces. On the other hand oradditionally, a combination of tetrahedra and octahedra do fill space(Steinhaus 1999, p. 210; Wells 1991, p. 232). In addition, octahedra,truncated octahedron, and cubes, combined in the ratio 1:1:3, can alsofill space (Wells 1991, p. 235). In 1914, Föppl discovered aspace-filling compound of tetrahedra and truncated tetrahedra (Wells1991, p. 234).

There seem to be only five space-filling convex polyhedra with regularfaces: the triangular prism, hexagonal prism, cube, truncated octahedron(Steinhaus 1999, pp. 185-190; Wells 1991, pp. 233-234), andgyrobifastigium (Johnson 2000). The rhombic dodecahedron (Steinhaus1999, pp. 185-190; Wells 1991, pp. 233-234) and elongated dodecahedron,and squashed dodecahedron appearing in sphere packing are alsospace-fillers (Steinhaus 1999, pp. 203-207), as is anynon-self-intersecting quadrilateral prism. The cube, hexagonal prism,rhombic dodecahedron, elongated dodecahedron, and truncated octahedronare all “primary” parallelohedra (Coxeter 1973, p. 29).

In the period 1974-1980, Michael Goldberg attempted to exhaustivelycatalog space-filling polyhedra. According to Goldberg, there are 27distinct space-filling hexahedra, covering all of the 7 hexahedra exceptthe pentagonal pyramid. Of the 34 heptahedra, 16 are space-fillers,which can fill space in at least 56 distinct ways. Octahedra can fillspace in at least 49 different ways. In pre-1980 papers, there are forty11-hedra, sixteen dodecahedra, four 13-hedra, eight 14-hedra, no15-hedra, one 16-hedron originally discovered by Föppl (Grünbaum andShephard 1980; Wells 1991, p. 234), two 17-hedra, one 18-hedron, sixicosahedra, two 21-hedra, five 22-hedra, two 23-hedra, one 24-hedron,and a believed maximal 26-hedron. In 1980, P. Engel (Wells 1991, pp.234-235) then found a total of 172 more space-fillers of 17 to 38 faces,and more space-fillers have been found subsequently. P. Schmittdiscovered a nonconvex aperiodic polyhedral space-filler around 1990,and a convex polyhedron known as the Schmitt-Conway biprism which fillsspace only aperiodically was found by J. H. Conway in 1993 (Eppstein).Thus, mathematical tessellation is complex. In the current invention, Inaccordance with embodiments substantial tessellation may already besufficient. In accordance with embodiments, elements may be providedwith sealing provisions that enable filling of remaining spaces betweenelements.

Elements may be combined into an object by placing elements on top ofone another. Elements may also or additionally be held together byallowing at least some of the elements in an object to exert anattracting onto other elements in the object. When combining elementsinto an object, the elements may be placed substantially on top of oneanother. Thus, elements may align in three dimensions.

Alternatively, for instance for providing more cohesion, the elementsmay be combined in a bond. For instance, in two dimensions (in fact, onedimensional), in stretching bond, or another known bond. These bonds arein general known to a skilled person. These bonds can also begeneralised in three dimensions. Thus, faces can overlap partially inone direction. In the other two directions, elements align. Bonds canalso be designed in two directions. Thus, planes of elements arecreated. Bonds can even be designed in three directions, creating athree-dimensional bond. Faces may, for instance, overlap with onlycorner parts.

In elements of the current invention, in accordance with embodiments theelements all have the same shape allowing them to substantially fill aspace. Gaps may remain. In such instances, elements may be provided withgap-sealing provisions. In accordance with embodiments, to allowelements to displace with respect to one anther without help fromadditional elements, the elements comprise motion modules guidingmodules and motion restriction modules on each face.

The above-explained inter-face symmetry and the intra-face symmetry maybe combined. Furthermore, these face symmetries may be combined with theshapes mentions above. Thus, face symmetry and shape symmetry mayprovide an additional flexibility in controlling, displacing, andbuilding objects.

In accordance with embodiments, the motion module, motion guiding moduleand motion restriction module are designed in such a way that that anelement that has two opposite neighbours to move with respect to thoseneighbours in a direction away from those neighbours while theseneighbours maintain their position. In particular, this is the case whenthe element was at first coupled to its neighbours. Before moving awayor displacing, the element detached from the neighbouring elements. Morein particular, an element is designed in such a way that it issurrounded by at least four neighbouring elements surrounding theelement and at first coupled to the element, to move in a direction awayfrom the neighbouring elements. This is easiest explained based onelements that are block-shaped and have the same size.

Suppose the 9 block-shaped elements form a block object of 3×3 elements.The elements are in face-contact and motion restriction modules couplerespective elements of the 9 elements together in such a way that theyform one object in the shape of a block. Then there is one centreelement that has 4 elements that are in face-contact with the centreelement, and there are four ‘corner elements’. If the centre elementwants or needs to move out of the 3×3 block while the other elementsremain coupled and in position, the centre element needs to displace ina direction that is perpendicular to a plane of the object. In such asituation, for instance motion restriction modules of relevant elementsmay be actuated in such a way that the centre element is no longercoupled to the other elements. Now, motion modules can be actuated toset the centre element in motion.

The elements are for instance symmetrical, for instance having threeorthogonal mirror planes. When the elements are block-shaped, easystacking is possible.

The person skilled in the art will understand the term “substantially”in this application, such as in “substantially encloses” or in“substantially extends up to”. The term “substantially” may also includeembodiments with “entirely”, “completely”, “all”, etc. Hence, inembodiments the adjective substantially may also be removed. Whereapplicable, the term “substantially” may also relate to 90% or higher,such as 95% or higher, especially 99% or higher, even more especially99.5% or higher, including 100%. The term “comprise” includes alsoembodiments wherein the term “comprises” means “consists of.”

Furthermore, the terms first, second, third and the like if used in thedescription and in the claims, are used for distinguishing betweensimilar elements and not necessarily for describing a sequential orchronological order. It is to be understood that the terms so used areinterchangeable under appropriate circumstances and that the embodimentsdescribed herein are capable of operation in other sequences thandescribed or illustrated herein.

The construction elements herein are amongst others described duringoperation. As will be clear to the person skilled in the art,embodiments are not limited to methods of operation or devices inoperation.

It should be noted that the above-mentioned embodiments illustraterather than limit the invention, and that those skilled in the art willbe able to design many alternative embodiments without departing fromthe scope of the appended claims. In the claims, any reference signsplaced between parentheses shall not be construed as limiting the claim.Use of the verb “to comprise” and its conjugations does not exclude thepresence of elements or steps other than those stated in a claim. Thearticle “a” or “an” preceding an element does not exclude the presenceof a plurality of such elements. Embodiments may be implemented by wayof hardware comprising several distinct elements, and by means of asuitably programmed computer. In the device or apparatus claimsenumerating several means, several of these means may be embodied by oneand the same item of hardware. The mere fact that certain measures arerecited in mutually different dependent claims does not indicate that acombination of these measures cannot be used to advantage.

Additional features described may allow increasing complexity of thesystem, or may allow elements to function more or less autonomous.Elements may group together to perform tasks, possible by features thatall the elements have, or using one or more features that only one orpart of the elements have.

Embodiments further relate to construction element or parts thereofcomprising one or more of the characterising features described in thedescription and/or shown in the attached drawings. Embodiments furtherrelate to a method or process comprising one or more of thecharacterising features described in the description and/or shown in theattached drawings.

The various aspects discussed in this patent can be combined in order toprovide additional advantages. Furthermore, some of the features canform the basis for one or more divisional applications.

DRAWINGS

Embodiments will now be described, by way of example only, withreference to the accompanying schematic drawings (which are notnecessarily on scale) in which corresponding reference symbols indicatecorresponding parts, showing an embodiment of a construction element,and showing in:

FIGS. 1A-1F a perspective view showing several subsequent steps of anexample of mutual displacement of three elements.

FIGS. 2A-2E a perspective view of several subsequent steps of anotherexample of mutual displacement of in this case four cube-shapedelements.

FIGS. 3A-3R a perspective view of several subsequent steps of anotherexample of mutual displacement of in this case 18 cube-shaped elements,and in FIGS. 3N-3P 26 elements.

FIGS. 4A-4D relate to various possible motion modules, motion guidingmodules, motion-restriction modules and combinations thereof, in whichin particular:

FIG. 4E-4L shows a combined motion module, motion-guiding module andmotion-restriction module.

FIG. 5A-5C show a motion module based upon magnetic forces.

FIG. 6A-6D shows a separate motion module and motion-guiding module.

FIGS. 7A-7D show an alternative combination of motion module,motion-guiding module and motion-restriction module based uponpiezo-elements.

FIG. 8 shows a schematic drawing showing modules that may be present inan element, and the interconnection between modules.

FIGS. 9A-9K Show the use of a separate, shared motion module.

FIGS. 10A-10H show a motion module that can change its orientationinside an element.

DESCRIPTION

In this detailed description of embodiments, elements have a generalreference number 1, and will individually be indicated with letters ‘a’,‘b’, . . . in order to distinguish them from one another. In thediscussion, the reference number 1 will be left out when referring toelement ‘a’, ‘b’, etc. The elements a, b, . . . can be identical. Theycan also differ in shape or functionality. The elements have a centre 2(only indicated in element b of FIG. 1A). This centre can in general bea centre of mass (also referred to as “centre of gravity”), oralternatively a geometrical centre (also referred to as “centroid”) ofan object. If an element has a uniform density, the centre of mass isthe same as the centroid.

Each element 1 can have one or more faces 3 that are adapted to allow anelement 1 to be positioned on or against another element 1. Inparticular, the one or more faces 3 can be adapted to allow elements 1to displace with respect to one another with the surfaces of face 3 incontact or almost in contact. In this detailed description, however,other options will also be demonstrated.

First, some examples of elements and displacement of elements withrespect to one another will be demonstrated.

In FIGS. 1A-1F, three elements a, b, and c are of a triangular shape. Inthis embodiment, each element 1 has at least one face 3 with a surfacethat allows the elements to be in contact with one another and todisplace with respect to one another over the surface of these faces 3.This at least one face 3 of elements 1 thus have a surface 3 that isadapted to allow for an element a, b, c to displace over another elementa, b, c. In element b, a centre 2 is indicated. For the discussion, thenature of this centre 2 is not important: A centre 2 has a fixedposition in its corresponding element 1.

FIGS. 1A-1F show an example six subsequent steps of element c withrespect to elements a and b. Elements a and b remain at the sameposition and orientation with respect to one another.

In FIG. 1A, starting positions of elements a-c are depicted. Element cstarts from a position in which it is in contact with the surface of oneface of element a only. Element c starts to move to the right side ofthe paper. In FIG. 1B, element c is moving to the right and ispositioned between elements a and b, and continues to move to theright-hand side of the drawing. In FIG. 1C, element c is no longer incontact with element a, Element c now is in contact with the surface ofa face 3 of element b only. Element c continues to move to the rightside over the surface of face 3 of element b, and in FIG. 1D it arrivesat an end of the surface of face 3 of element b. Element c is able tomove on to the right and in FIG. 1E, it arrives at a position depicted.In this position, halve the area of the surface of face 3 contacts thesurface of face 3 of element b. Element b now starts moving in adirection into the paper and cross with respect to the earlierdirection.

In FIG. 1F, element c is shown in a rest position. In this position, asurface of face 3 is only partly in contact with the surface of face 3of element b.

In the example of FIGS. 1A-1F, the elements a-c exert forces on oneanother using the motion modules, motion-guiding modules and/ormotion-restriction modules. These forces can be exerted mechanically,using electromagnetic forces, using chemical forces, and any otherphysical forces, or a combination of these. In case of a chemical force,a potential use of a reversible process which for example does not leavetraces on a surface may prolong the usability for future movement alongsuch a surface. When describing the movement phases it must beunderstood that movement may vary in speed and acceleration. Even aninterrupted sequence of move, no move and move again is possible. Whenmoving or not moving, an element may withstand one or more forcesexerted upon that element (internal or external) selected from the groupconsisting of for example gravitational force, mechanical force,electrical force, chemical force and climate forces. A potential use foran element is for example on a different planet, in a fluid or in avacuum like outer space.

Alternatively, element c is held on elements a and b via a mechanicalmeans or via for instance magnetic force. In this example, the surfacesof the faces 3 of the elements a-c may actually be in contact with oneanother. Below, various embodiments of motion modules, motion-guidingmodules, and motion-restriction modules are illustrated and which may beused for the motion shown in FIGS. 1A-1F.

In the example of FIGS. 2A-2E, four elements 1, indicated a-d, areshown. These elements a-d displace with respect to one another. Theelements 1 in this example are identically shaped cubes. In thisexample, the faces of the cubes are solid surfaces and the cubes rest oneach other's solid surface and can be under the influence of agravitational field. A starting position of the elements a-d isindicated in FIG. 2A. If the displacement action indicated in FIGS.2A-2E would be repeated, the construction of four elements a-d as awhole moves to the right.

In FIG. 2A, element a starts displacing along a surface of face 3 ofelement b in an upward direction. Element a thus displaces towardselement d. In fact, centre 2 of element a moves away from the centre ofelement b and gets closer to the entre of element d when it moves in theupward direction.

In FIG. 2B, element a arrived at a position closest to the centre ofelement d. Element a now no longer contacts element b. Now, elements aand d together start displacing to the right side of the paper. This maybe done in several ways: Element a may couple to element d, and a motionmodule of either element d or element b starts acting on element d inthe direction of (intended) motion. This results in a motion of elementsa and d. When elements a and d displaced so much to the right that asurface of face 3 of element a now contacts part of the face 3 ofelement b. Now part of a motion module of element a may engage part of amotion module of element b. In such a stage, the combined motion ofelements a and d may be caused using the motion module of element a,element b or element d, or combinations of these motion modules.

In FIG. 2C, elements a and d are exactly on top of elements b and c.Elements a and d continue to displace together to the right until thesituation depicted in FIG. 2D is reached. There, elements a and d stop.Now, element d starts displacing in a downward direction, with itscentre moving away from the centre of element a and towards the centreof element c. Again, this motion can be caused by the action of a motionmodule of element a, of element c or element d, or a combined effort ofany of these motion modules.

In FIG. 2E, the elements a-d are in fact in a similar externalconfiguration. Thus, in fact the same construction as in FIG. 2Aresults, but displaced to the right with a displacement which equals thelength of a side of an element. Next to having displaced elements a-danother additional aspect of embodiments will be described:transportation. When an object is temporarily coupled to element a, forexample placing a basket with material on top or inside element a;element a now uses it's own or the other elements movement ability totransport this other object from one position to another position.Alternatively, an element may comprise a build-in storage space. Thus,the element may functionally be or comprise a container for holdingmaterial.

In FIGS. 3A-3H, a construction of 18 elements 1 in fact changes itsshape by moving elements with respect to one another. All the elementshave an identical shape. The functionality of the elements may differ.Thus, the functionality of the new construction may also differ.

In the arrangement of 18 elements 1, the top 9 elements are indicateda-i. In order to get to a new arrangement of these elements depicted inFIG. 3H, many schemes are possible. FIGS. 3B-3G show severalintermediate arrangements of the elements. One of these possible schemesis to first displace the complete row d-f two positions to the left(FIG. 3C), then displace element c to the left until its centre isclosest to element e (FIG. 3D), then displace element f in a positionwhere its centre is closest to the centre of element c (FIG. 3E), thendisplace the elements c and f to the left until elements b and c touch(and may lock) (FIG. 3F). Then displace element e down until it reachesthe position shown in FIG. 3G. This can be done using the (or part ofthe) motion module of element d, f, the element below element d, andelement e, or a combined action of a selection of these elements. Next,element d moves to the left until the configuration of FIG. 3H isrealized. This scheme thus requires 7 steps, displacing a total of 4elements (c, d, e, f) a total of 12 positions: when going from FIG. 3Ato FIG. 3B, a displacement of three positions occurs, from FIG. 3B toFIG. 3C three positions, from FIG. 3C to FIG. 3D one position, from FIG.3D to FIG. 3E one position, From FIG. 3E to FIG. 3F two positions, fromFIG. 3F to FIG. 3G one position, and from FIG. 3G to FIG. 3H again oneposition. This adds up to a total of 12 positions. The same endsituation or configuration of elements can also be reached in anotherway. This is shown in FIGS. 3I-3O. First elements a-c are displacedtogether one step along elements d-f to the left as in FIG. 3J.Subsequently (FIG. 3K), element f is displaced in the direction into thepaper until its centre is at its closest position with respect to thecentre of element c.

Next, in FIG. 3L elements a-f move as a group one position to the right.Alternatively, a, b, c, f move as one group and d, e move as a secondgroup. Speeds may differ. Next, element e moves to the right (FIG. 3M).FIG. 3N depicts the intermediate position of element e while movingdown; in this position element e uses element f and in parallel orsequentially uses the element on the left side of element e.Subsequently the composition of FIG. 3O is again realized. This schemerequires five steps (not counting FIG. 3N), displacing 6 elements (a-f)a total of 12 positions. The last scheme may require a smaller amount of(kinetic) energy, for instance element d has now been displaced only 1position.

In FIGS. 3P-3R, it is illustrated how an element 1 can move when it issurrounded by other elements 1. Here, in FIG. 3P 26 element 1 areassembled into a single cube, with one free space in the right centrerow of elements 1. The 26 elements thus form one object: a cube with oneopening. In FIGS. 3P-3R, the top 9 elements 1 are lifted only forillustration purposes. Element ‘e’ is thus in FIG. 3P in face-contactwith 5 other elements 1, including elements ‘b’, ‘d’, and ‘h’. Themotion module, motion guiding module and motion restriction module inthis embodiment allows the element ‘e’ to move to position 3Q andfurther on to the position indicated in FIG. 3R while the other elements1 remain at their position. Below, several examples are presented ofembodiments of the various modules. These modules, or variationsthereof, allow an element (or clusters of elements) that is (are) atseveral sides enclosed by other elements, to leave an object or displacewithin an object. In the example of FIGS. 3P-3R, the motion module ofelement ‘e’ will use the motion guiding module of at least one of theelements with which it is in ‘face contact’. In accordance withembodiments, in order to prevent element ‘e’ from getting blocked,element ‘e’ may use the motion modules of all but its faces 3 that areeither facing away from a direction of motion, and its face 3 that facesthe direction of motion. In a situation where the object is subjected toa gravitational force working in the direction towards the bottom of thedrawing, it may be conceivable that only a motion module in/at the lowerface (opposite the face that carries the identification ‘e’) isoperative. To get to the position indicated in FIG. 3R, the motionmodule of element ‘e’ In accordance with embodiments subsequently usesfor instance motion guiding modules of the element 1 directly belowelement ‘e’ in FIG. 3P, and/or the element 1 below element ‘e’ in FIG.3R, or a combination of the two if possible. Alternatively or incombination, element ‘e’ may also use motion guiding modules and/ormotion modules of elements b, c, h, i if possible. In general, it mayuse motion guiding modules and/or motion modules of elements in contactwith element ‘e’.

When comparing end positions and the way that theses end positions areaccomplished, several aspects can be taken into account. At a highestlevel, the performance of the system of elements as a whole may beevaluated. At a lower level, the performance for a group of elements maybe evaluated. At the lowest level, the performance of a single elementmay be the subject of performance evaluation. These aspects for instancemay have to do with the (in)equality of elements, element limitations,principles on how to handle forces acting upon an element andinter-element, required intermediate positions, principles used fornavigation or problem solving, the speed at which a certainconfiguration of elements is being reached, energy consumption.

To achieve a certain position fuzzy logic, artificial intelligence, datamining techniques, machine learning, (path finding) algorithms,proportional logic, game theory, or other methods known in the field maybe used. Elements may be steered or controlled from one or more centralpoints. Alternatively, elements may be adapted to make their owndecisions. In yet another alternative, elements may use distributedcontrol. Thus, several degrees, levels or combinations between beingsteered or controlled and making own decisions are possible. Thus, anelement or a group of elements can operate autonomously, for instanceusing data or information obtained from other elements and/or othersources. An element can have agent functionality and may learn from thefeedback of its environment. An element may investigate, by computation,several potential actions or sequence of actions it is able to make.Subsequently, the element may determine either for itself, or for one ormore other elements, which action has the highest benefit to theelement, or to one or more other elements. It may then select thataction or sequence of actions, and execute that action or sequence ofactions. Furthermore, the timing of an action or sequence of actions maybe taken into account: Elements may be planning their sequence ofactions wherein the planning may take into account actions from otherelements, or it may anticipate actions by other elements. Elements mayreceive only part of the information needed to accomplish a finalconfiguration of elements and therefor need to communicate to otherelements or devices. Client-server, master-slave, peer-to-peer, push orpull systems, polling, swarming- or other (hybrid) methods/technologymay be used or adapted. Sometimes parallel movement (of individualelements or groups of elements) occurs next to sequential movement. Sothe movement of element d and element e to their final position couldhave occurred in one step from FIG. 3F directly to 3H at the same timeinstead of sequentially as described in the current FIG. 3F followed by3G (movement of element e) and 3H (movement of element d). Sometimes acertain configuration of elements can only be reached by a method whereone element is helping another element. A helper element can temporarilybe inserted and used, then retracted from the other elements and thusnot have a position in the final configuration of elements at all. Dueto the reusability of the elements a large number of configurations ofelements can be achieved over time. Well-designed elements do not haveto be recycled but can be re-used, even for different purposes. Thislowers the burden on our natural environment in several ways. If anelement in an object does not function properly or is broke, it mayeasily be removed, for instance by actions of other elements, andreplaced with a functioning element. The element may also be serviced.

A set of elements can assume a first configuration, and then move withrespect to one another into a second configuration. Thus, the set ofelements together are first in a first shape, and then in a secondshape. This is also referred to as ‘shape shifting’. In this process,the elements may be reused.

This shape shifting by displacing reusable elements allows for examplethe formation of a table from a group of elements. When at a later stagethis table is not required any longer, at least one element from thegroup can be instructed to exert some form of control over, or tocommunicate to, at least one other element of the group. This can bedirect, wireless, but may also be accomplished by for instance amessenger element which can be inserted or added and which transfers themessage to an element out of the group and then returns. A task of thegroup of elements may thus comprise changing its current shape, forinstance a chair, into a table, and back again into a chair.

Thus, the elements start moving with respect to one another. Theconstellation of elements that first fulfils the requirements of a chairshifts its shape to a constellation that fulfils the requirements of atable. The constellation of elements can then reorganise itself tofulfil the requirements of a chair according to input given or alreadyavailable at an element. Thus, the task of reusing the elements isexecuted by the elements.

Interaction with a human being exerting physical control, for examplepicking up, stacking, or replacing one or more elements, is not needed.This is a different method than building constructions with for instanceLego, in which human interaction is required. It is clear in thisexample that some form of intelligence or rules regarding mechanics,construction, architecture may be applied by an element or given to anelement by a device, such that a person can actually use the chair tosit upon without the chair falling apart due to for instance thedisintegration or disconnection of connected elements.

The elements can be physical at various scales. First, their size canvary. Their size may be comparable to playing blocks. Thus, an elementmay have a cross section of between 1-5 cm. An element may be a buildingblock for constructing a building. In such an instance, a building blockmay have a cross section of about 5-50 cm. The elements may also be sosmall that the human eye can hardly discern the individual element. Insuch an embodiment, an element can have a diameter smaller than 1 mm. Inparticular, the diameter can be smaller than 100 micron. This mayrequire the use of nanotechnology and for instance molecular or atomicmotors. These elements can be used to build parts of this invention, ascan larger elements the size of bricks or prefab concrete elements thatmay form a building. When leaving out the physicality of the elements,the elements can be simulated in order to determine or predict whether aconfiguration of elements can be achieved. In order to achieve a goalstate when starting from a begin or start state, an element may need acombination of a program or app, with functionality which allow somefunctions to be performed. These functions steer actuators available inan element. Available sensors may give the element or the program input,potentially resulting in a different outcome of a function or a group offunctions. These attributes and interactions as such may be known in thefield of robotics.

From this a game or simulation, may be construed, which may be usingphysical or virtual elements or a combination of both. In such a game,it can be the task of a player to select the right program and the rightfunctions/functionalities in order for elements to achieve a certaingoal state out of a begin state. This game can be played by a humanbeing alone, or by a computer. It may be played by at least one humanbeing against at least one other human being or against at least oneother computer, or a combination thereof.

Specific parameters measure the success; parameters like consumption ofenergy, speed, amount of moves of an individual element or of the groupas a whole, amount of memory/cpu usage, strength of the goal state, ortime required to reach the end state. When applying this with a certaindegree of autonomy of elements and randomness for example by usingartificial intelligence, the outcome may in advance not be known to aplayer. An overkill of regulating constraints to an element may restrictan elements ability to respond well to other situations/goal states;there may also be a trade-off between specialization and generalization.A player can for instance design on a game device a certain goal stateand give certain elements selected properties: a selection from a groupof programs, of actuators or motion modules, of sensors, of functions,of energy systems, and of communication systems. It must be understoodthat these properties of an element may act on other elements ordevices. The design can be used by at least one element. The design isprovided in part or as a whole to one or more elements and the elementsstart the displacement and depending upon the given properties thedesign, actually being a goal state can be accomplished or not. Changingthe design allows for the elements to try to achieve another goalposition. The elements can be physically or virtually, and displacethemselves according to the given properties. Elements may be configuredin order for the elements to exchange at least one property orfunctionality with one another or with another device. Elements maycomprise memory in order to recall previous situations or computepotential future situations. This as such is known in the field ofcomputer science. A goal state can be defined in different ways. Forinstance, the outer boundaries of a set of elements can be used as agoal state. For example, the end shape is a cube, or a plate.

The goal state may be functionally defined at element-level. Forexample, each element must have at least one face in contact withanother element; each element must have at least 2 faces free.

A goal state may also be a list of locations, absolute or relative toother elements, of elements, or for instance specific elements havepredefined end positions, again either relative, absolute, or acombination of both.

A goal state may also be represented by a mathematical function, generalor mathematical demands or requirements on an assembly of elements, forinstance, the assembly or configuration of elements must have aparticular plane of symmetry, a hollow space inside, a definedcircumference, a defined volume, number of layers, etc.

A goal state may also be functional. Elements having a definedfunctionality or property are at a certain position. Or the positionshould be such that the function is optimized. For instance, elementshaving a photovoltaic face should be located and/or positioned such thattheir production is maximized. The goal state may even evolve, change orbe modified, even during the motions of elements towards the originalgoal state. The goal state may for instance change due to environmentalinfluences, like day/light rhythm, temperature, etcetera, or may betime-dependent. A goal state may also be a negative definition, or be anexclusion.

Additionally, outside interaction may be possible. For example,inserting or removing an element to or from a certain state. This may bedone physically for instance by a human being by using his/her hand.When done by taking into account how elements may attach/interact to oneanother, an element adjacent to a newly added element may notice/sensethis interaction and use this for its own and potentially for otherelements' behaviour in the configuration of elements. When going back tothe example of designing a goal state on a device, the inserting orremoving of at least one element may be taken into account by thatdevice as well. Alternatively, a predesigned goal state may be used.

An example of this is a child designing a castle using the elements.Imagine the child using a computer device. There are many examples ofusable devices. For instance, a handheld device, such as for instance ahandheld device comprising a (touch)screen. An example of such a devicecomprises a smartphone, an iPad, a smart watch or similar device. Thesedevices may receive user input via a touchscreen, voice control,receiving muscle or nerve input, or other input means.

Suppose a castle is constructed using elements. Physically, the castleformed in a room by action and displacement of the elements themselves.After or during said formation, the child extends the castle byphysically adding two more elements. A device may for instance comprisean “app” running on a device like the iPad, which receives informationfrom an element forming part of the castle that the two elements areadded. The child may save his/her altered version of the castle. Whendone playing, the child instructs the elements by means of the app tomove to a certain begin state. Such a begin state may be compact so thathis/her room may be used for other purposes. This example may then usewireless communication or multiple devices, like for instance multipleiPads, which are used to make a joint configuration of elements even atremote or uninhabited locations (like on planet Mars).

Another goal may be the following. Due to for instance displacement or achange or orientation of one or more elements, conditions may beoptimized. For example, the elements may optimize growing conditions forplants. This may be achieved by for instance physically moving one ormore plants, providing shade by covering the sun. Two assemblies ofelements can displace two plants or groups of plants with respect to oneanother in such a way that the growing conditions for both plants areoptimized. In accordance with embodiments, elements may form acontainer, for instance a pot, holding the plants. In such a container,one or more elements may for instance provide an opening in thecontainer for allowing excess of water to flow out of the container.Parts of the container may form a sunshade, or the elements maycompletely move the plant.

Communication may replace a certain type of sensor functionality. Anelement may use a sensor to detect only its direct neighbour.Alternatively, a sensor may be able to detect another element twopositions further, or an element may ask or receive information from another element if that other element is in contact with the element twopositions further. Sensors can use contact/proximity detection by usingthe electromagnetic or the audio spectrum.

Another example is when two users play a game on for instance twoseparate devices, for instance on two iPads, two users play a game inwhich reaching a certain given goal state physical or virtual is thepurpose of the game. As described earlier, this can be accomplished byselecting the right properties, functionality or tools for the elements.In this game there may be limits on certain properties or limits on howmany different element configurations can be used for a certain goalstate when playing a level of that game. An approach akin to the programMinecraft or other virtual worlds can be accomplished with for instancethe difference that the current elements may physically build what isvirtually designed when using design rules applicable to a physicalelement.

In FIGS. 4A-7C, various embodiments of motion modules, motion-guidingmodules and motion-restriction modules are illustrated. Theseembodiments are examples showing ways to work embodiments for physicalelements 1.

In FIGS. 4A-4C, a cross-sectional view, detail and top view are shownwhich illustrate a mechanical solution that combines a motion module, amotion-restriction module and a motion-guiding module. In FIG. 4B, across section is shown of parts of two elements 1, 1′ that arepositioned on top of one another. Faces 3 are almost in contact. Infact, if their surfaces have little to almost no friction, the surfacescan in fact be in contact. Otherwise, one of the three modules (motion,motion-guiding and motion-restriction) will cause a little distancebetween the faces 3.

In the embodiment of FIGS. 4A-4C, an embodiment of part of two elements1 is schematically shown. Part of the motion module 10 of element 1 is aretractable wheel. Another part of the motion module is the part oftrack 11 that provides an engagement surface of the tread of theretractable wheel. The track 11 further provides part of the motionguiding module and of the motion restriction module.

Element 1′ has in this embodiment the same modules. FIG. 4A shows oneelement in top view, and FIG. 4B shows a cross section of FIG. 4A asindicated, but with a second element on top of it and also crosssectional view.

In FIG. 4B, the retractable wheel of element 1 extends and engages amotion guiding module of element 1′, here track 11′ of element 1′.Retractable wheel 10′ of element 1′ is here in its retracted position.Retractable wheel 10 of element 1 in its extended position engages track11′. In element 1, in order not to hinder the retractable wheel 10, aslidable cover 12 is in its inactive position. It slides here to theright in the drawing. Element 1′ has its slidable cover 12′ closed. Inthis embodiment, the cover 12′ together with track 11 provides acontinuous track. The track 11 is sunken with respect to the surface orface 3. In FIG. 4C the motion module is shown in more detail. The motionmodule 10 comprise retractable wheels, comprising a strut 18 coupled toa shaft 16 that is cross with respect to strut 18. In this embodiment,shaft 16 carries wheel 17. A driving motor for the wheel 17 here is anelectromotor 19 that can be provided as a rim motor inside wheel 16.Alternatively, the electromotor may be provided in shaft 16. Here atopposite ends of shaft 16, parts 15 of the motion-restriction module areprovided that many be extended and retracted in the axial direction ofshaft 16. In extended position, it can engage in a groove 14 (FIG. 4B),and in retracted position the motion module 10 can be retracted.

In FIG. 4A, only one face of an element is shown. In accordance withembodiments, of which parts are already discussed above, the element 1may be a cube. Such a cube can be provided with six similar faces. Infact, the six faces may also be identical. In the embodiment of FIG. 4A,a face carries a cross shaped track. Here, the centre of the cross islocated at the centre of the face. In accordance with embodiments, theelement may have further faces that are provided with a similar,cross-shaped track. In order for elements to be able to displace withrespect to one another in a flexible way, the track on one sidefunctionally connects to the track on another, neighbouring face. In theexample of FIG. 4D element 1 has one single, closed, sunken, track thatruns all around four sides or faces of the element 1. In this drawing,groove 14 differs from the embodiment of FIGS. 4A and 4B. One of thewalls of the groove 14 runs equal with the surface of track 11. In theembodiment of FIG. 4A, the element has at least two tracks. These trackshave two crossings at opposite faces, and in FIG. 4A one of thecrossings is visible.

Now suppose two elements 1 of the type shown in FIG. 4A that arepositioned with their face in contact. In order for a third elementhaving the wheel as shown in FIG. 4B to move over the face of oneelement 1 and continue over the neighbouring element 1, A similarneighbouring element must have a similar sunken track at the same levelto allow the moving module to traverse the two gaps (each elementcausing one gap. It may also be seen as one single gap). FIGS. 4E-4Lschematically depict 3 elements 1; a, b and c, in a cross-sectionparallel through the centre of the tracks of the elements. The gaps inthe lines resemble the gaps of FIG. 4D of the closed track around theelement. FIG. 4E shows that the extended wheel module 10 of element ‘a’is running in the track of element ‘b’. FIG. 4F depicts the situationwhere the wheel module 10 tries to traverse the first gap. It is obviousthat there is no traction by which the wheel module can displace element‘a’ any further in the direction of element c by itself. One or morehelper elements 1 attached to element 1 ‘a’ may in this case solve thatproblem. Potentially the element 1 of FIG. 4D has a different motionmodule 10: a motion module 10 with multiple wheels (FIG. 4G). First sucha motion module 10 extends towards the track. Subsequently the motionmodule 10 extends its wheel base length and two wheels will be followingthe track. In this embodiment, a frame connecting both wheel axesextends. The wheels in FIGS. 4G and 4H may have half the width of thesingle wheel of FIG. 4E. In that way, these wheels if the embodiment ofFIGS. 4G and 4H can slide out of one another and fit into the track. Thedistance between the rotational axes those two wheels is such that thetwo wheels span the two gaps, which is depicted in FIG. 4H: When onewheel has no traction, the other wheel has traction. The distancebetween the rotational axes of the two wheels may be set. These twowheels may be jointly or independently of one another use a motorizedpart.

In another embodiment, multiple motion modules 10 are provided at acertain distance from one another. This allows for movement while one ofthe motion modules 10 crosses the two gaps and another motion module 10moves over track 11 (FIG. 4I-4L).

FIG. 4I shows an element 1 having two extended motion modules 10 whichare moving element a on element b and towards element c. In FIG. 4J theright wheel has no traction any more, due to the first gap. The leftwheel uses its power to continue the displacement of element a. In FIG.4K the second gap is reached. Still, the left wheel engages element band pushes element a further towards element c. In the situation of FIG.4L, both wheels have traction again: with the left wheel engagingelement ‘b’ and the right wheel engaging element ‘c’. The wheels maychange roles if element ‘a’ is completely on top of element ‘c’.

In the embodiment of a cube-shaped element, in fact three continuoustracks are provided that encircle the cube and that cross one another.Each track usually crosses the other track at two crossings. In fact,more tracks are possible that each have other advantages. In particular,an embodiment will be demonstrated in which one or more tracks can bemade over a face at almost each chosen path over the face. In thisdocument, such an embodiment is provided using magnetic parts. Specificother layouts of track that are mentioned here are providing a face withtwo sets of two tracks. Each set crosses the other set. The tracks of aset can be provided symmetrically with respect to the centre of a face.Thus, in fact the tracks are laid out in the shape of a #-sign. Inparticular, two sets of parallel tracks are perpendicular with respectto one another. When providing a cross-shaped track an element, inparticular, when it is a cube, can usually only move on another elementwhen a face of both elements face one another, are parallel to thedirection of motion. In particular, these faces are in-plane. Thus, whenanother motion is required, the help of another element may be needed.An advantage of the cross-shaped track is the relatively simple layout.Furthermore, motion can be provided using a single motion module on eachface, at the crossing of a track. Thus, in the embodiment of a cube, sixmotion modules may be needed to enable full motion capability. In theembodiment of FIG. 4A, each track 11 is provided with four motionmodules. This may be needed to provide sufficient traction, supplemotion. Other placements of motion modules in the track may be possible,and another number of motion modules per track may be used. In a simpleembodiment, already mentioned, one motion module at a crossing of atrack may be sufficient under certain conditions.

FIG. 4B shows in schematic cross-section an embodiment in which a motionmodule 10 is shown in more detail. In this embodiment, a part of themotion module 10 is an extendable driving unit that can move up and downwith respect to a face 3, 3′. It can be retracted, leaving the face 3free, and it can be extended in order to extend beyond the surface of aface 3 and to engage a track 11 of another element.

In this embodiment, many ways can be devised to provide amotion-restriction module. Furthermore, many ways can be found toprovide a motion-guiding module. In this embodiment, a mechanicalsolution is presented. Thus, part of a motion-restriction module and amotion-guiding module are provided using a set of grooves 14 at bothsides of track 11. The grooves 14 here provide opposite normal abutmentsworking along a line normal to the face of an element, and oppositetransverse abutments working along a line in-plane with respect to aface and cross with respect to the track. In a simple embodiment, thegrooves 14 have a rectangular cross section. Here the grooves areparallel to the face, and parallel to track 11. Thus, the grooves 14together provide part of a motion-restriction module and amotion-guiding module. In fact, grooves 14 can be seem as partlyundercut grooves, comprising an undercut at both opposite longitudinalsides of the groove 14.

In this embodiment, another part of a motion-restriction module and amotion-guiding module is realized through parts 15 running in thegrooves 14. The parts 15 run in grooves 14 and provide abutments in thegrooves 14. The various principles shown here can be combined.

In FIGS. 5A-5C an alternative embodiment for the motion module, motionguiding module and motion restriction module is demonstrated. Thisembodiment demonstrates an embodiment that avoids mechanical means forrealizing a motion module, a motion-guiding module and amotion-restriction module. Parts of a non-mechanical embodiment and amechanical embodiment may be combined. This embodiment uses magneticforce. To that end, permanent magnets and switchable magnets may becombined.

The following embodiment can be realized in an element. In FIG. 5A, theelements 1, 1′ both comprise at least one strip of magnets 40 that canbe switched on and off. Thus, the parts in a strip can be selectablyactivated. In this way, the strips in two elements can together form adistributed linear motor. In fact, the principle of a linear motor assuch is known in the art. In this embodiment, such a linear motor issplit into two separate parts. This allows the motor to function as amotion module. Using the magnetic force, the opposite strips 10, 10′ intwo elements that are on top of one another with their strips above oneanother can even provide at least part of a motion-guiding module.

In this embodiment, additional strips can be provided at the surface ofan element. In accordance with embodiments, two strips can be providedin/at a face of an element. These strips can be substantially parallel.Thus, the strips can function as a motion module and amotion-restriction module. In accordance with embodiments, two elements1, 1′ are positioned one on top of the other. Both elements comprise twostrips of selectably activatable magnets 40 and that are parallel withrespect to one another. The strips of the one element are furthermoresubstantially parallel with respect to the strips of the other element.Now, if several opposite parts of the strip of two elements that rest ontop of one another are actuated in an opposite way, the strips can evenprovide a motion-restriction module. When activating the parts in oneelement in an opposite way with respect to parts in the strips of theother element, parts of the strip of one element are poled in one way,for instance north or south, and these parts are opposed by oppositepoles, i.e., respectively south or north, of parts of the strip of theother element. Thus, the strips now attract one another. In theembodiment described, a mode is illustrated in which both elementschange the polarity of their magnets and cooperate. In an alternativemode of operation, one element can change the polarity of its magnets,while the other element leaves the magnet poles static. The magneticforce of the magnets may be adjustable.

The elements may be provided with at least two strips of magnet parts 40at or near one face 3 and that are provided substantially in a cross. Assuch, this is discussed above in a mechanical embodiment. It may also bepossible to provide several strips at one face.

The use of selectably switchable magnet parts 40 can even be provided inthe following embodiment, providing control over the motion with respectto one another of two elements that rest one on top of the other. InFIG. 5C, an element is provided with a two-dimensional (2D) grid ofselectably activatable magnet parts 40 or magnet patches. Magnet parts40 may be integrated into the surface of a face 3 of an element 1, butmay also be provided below the surface of a face 3. When elements 1, 1′are placed one on top of the other with the faces 3, 3′ contacting oneanother, and the magnet parts of the elements are activated in acontrolled manner, this can provide a 2D motion module. When oppositemagnet parts 40 are activated in an opposite way, the 2D magnet parts 40that are provided in a grid provides a motion-restriction module. Byselectable activating magnet parts 40 in a 2D grind in one element 1 andin the opposite element 1 resting on to of element 1, the magnet parts40 in both 2D grids interact. When opposite magnet parts are poledoppositely, two elements are attached and stick together. Whensubsequent magnet parts are activated, the effect of a plane-motor isrealized. Subsequently activating magnet parts along a line over a face3 will move elements 1 with respect to one another along that line. Infact, the 2D magnet parts thus also provide a motion guidingfunctionality. Faster motion may be achieved by activating groups ofmagnet parts 40.

The 2D grid of magnet parts 40 and the strip of magnet parts 40 may becombined.

The magnet parts 40 may be provided below a low-friction surface of aface 3. For instance, a polymer material may be used. In particular,PTFE or a similar low-friction polymer material may be used.

In addition to the at least one strip and/or the 2D magnet parts grid,at least one mechanical motion module, motion-guiding module and/ormotion-restriction module may be provided. For instance, a mechanicalmotion-restriction module may be activated to at least temporarily fixthe position of two elements with respect to one another in a way thatdoes not require the use of an energy source.

In FIGS. 6A-6D, schematically a mechanical embodiment using a separatemotion module 10, a motion-guiding module 20, FIG. 6B in cross sectionen FIG. 6C in further cross section as indicated in FIG. 6B) and aseparate motion-restriction module 30 (FIG. 6D in cross section) isshown.

The motion module comprises a caterpillar track in each element 1, 1′.Caterpillar tracks 10 here engages caterpillar track 10′. In caterpillartrack 10, one driving wheels or elements extends in normal direction orface 3 until it engages the caterpillar track 10′. The caterpillar trackmay be one linear track along a face 3, and alternatively it is a pairof crossing caterpillar tracks laid out like in FIG. 4A.

The motion-restriction module 30 here is an extendable pin 31 that firstis activated to extend out into a slot 32 in the opposite element. Whenpin 31 extends in slot 32, it rotates about its longitudinal axis. Thus,a cam 34 extending from pin 31 in transverse direction is rotated intoundercut opening 35′ in slot 32′. Can 34 thus hooks into undercutopening 35′. It holds the distance between the elements 1, 1′.uThisholds element 1 in position with respect to element 1′. In accordancewith embodiments, slot 32′ is a groove running along face 3 and havingan undercut groove 35′, thus motion-restriction module keeps theelements on top of one another during motion. Both elements 1 and 1′ canboth have parts of the motion-restriction module.

Motion-guiding module 20 of element 1 here is a simple, straight pin 21running in a groove 22′ in an opposite element 1′. Thus, a trail alongface 3 is defined. In accordance with embodiments and to guide motioneven better, the transverse cross section of pin 21 is rectangular, inparticular, square. It fits in groove 22′.

In FIGS. 7A-7D, yet another alternative embodiment of the motion module,motion-restriction module and motion-guiding module is schematicallyshown. This embodiment is based upon the use of piezo-elements forrealizing parts of the modules mentioned. ‘Piezo’ is used to refer to anelement using the piezoelectric effect. As such, there are principleslike linear motors that are suited for application in the elements. Inthis embodiment, one type will be discussed.

In this embodiment, a rail 80 is provided. Furthermore, here four piezomodules 70 are provided. The piezo module is extendible, in FIG. 7B, across section as indicated in FIG. 7A shows the piezo module 70 ofelement 1 in retracted position and piezo element 70′ in element 1′ alsoin retracted position. The piezo modules 70, 70′ have two U elementsthat are interconnected by a piezo piece 72. When activated, length Lchanges and the distance between the U-elements also changes. FIG. 7Cshows a top view of a piezo module 70, and FIG. 7D shows a side view ofthe piezo module 70. The distance D between legs 71 and 71′ is such thatit fits over the thickened part 83 of rail 80. The inner parts of legs71, 71′, in particular, the outer ends, are here provided with clampingpiezo elements 73, 73′. When activated, these piezo elements 73, 73′move inward and reduce the space D between legs 71, 71′. Thus, allowingthe legs 71, 71′ to clamp on the sides of rail 80, in the undercutgrooves 82, 82′. Thus, when piezo elements 73, 73′ are activated, piezomodules 70, 70′ are fixed onto rail 80. Motion of piezo module 70 overrail 80 is possible by subsequent clamping of the U elements. Ifactivation of piezo piece 72 is out of phase with the activation of theU elements, motion is possible.

Thus, here the piezo module 70, 70′ together with rail 80 is motionmodule, motion-restriction module and motion guiding module.

Alternatively, the motion module may be based engaging elements using ahoist, winch, rack and pinion, chain drive, belt drive, rigid chain andrigid belt actuators which all operate on the principle of the wheel andaxle. By rotating a wheel/axle (e.g. drum, gear, pulley or shaft) alinear member (e.g. cable, rack, chain or belt) moves. By moving thelinear member, the wheel/axle rotates. Thus, elements may be put inmotion with respect to one another.

In FIG. 8, a schematic cross section of an element 1 is shown,indicating the various components that may be present in an element 1.In this cross section, four faces 3 are indicated. Element 1 comprises adata processing unit 100, a data communication unit 200, an energy unit300, a sensor unit 400, a motion-restriction module 600, a motion module500 and a motion-guiding module 700. Next to these modules other modulesmay be present: for example, an actuator which can move or rotate aretracted motion module within the element 1. The data processing unit100 may be able to work together with other data processing units 100 ofother elements 1 and distribute computational tasks to one another; Thismay be done in the form of distributed computing or cloud computing.

The waving arrows indicate that the various modules and/or units caninteract with the environment outside the element 1. For instance, asensor unit 400 can measure a physical parameter outside an element 1.

An energy unit 300 may be charged from a source outside element 1.Charging may be wireless, for instance inductive, or using conductivesurface patches, for instance.

A data communication unit 200 may transmit data to outside an element 1,or be able to receive data from outside an element 1. This may be datatransmitted by another element 1. It may be an element that is incontact with element 1. Data communication may be analogue or digital,be wireless via the electromagnetic spectrum, via sound or via otherknown wireless data transmission protocols, for instance zigby,bluetooth, WIFI, Near Field Communication (NFC) or the like.Alternatively, data communication may be physically using conductivepatches on the surface of the face 3 of an element. Using a sensor likea (digital) camera and analysing data taken by the camera is also apotential form of data communication; known examples are for instanceQR-codes or bar-codes. Communication can go across several degrees ofdistances, even inter-planetary. The energy unit 300 in this embodimentprovides energy to components (modules and/or units) in the element 1.This is indicated by single arrows running from the energy unit 300 tothe other units and/or modules. An energy unit 300 may be an energystorage unit, for instance a chargeable battery, an accumulator, acapacitor, for instance a super capacitor, or the like. Alternatively,the energy unit 300 may also be a power generator, which generatespower. Examples of such an energy unit 300 are a fuel cell, a combustionengine, a photovoltaic element, or similar energy unit 300.

A sensor unit 400 may comprise one or more sensors that are able todetect a physical parameter. Examples of suitable sensors are atemperature sensor, a proximity sensor that detects the presence and/ordistance of another element. A pressure sensor, an air-pressure sensor,a light sensor, a location sensor (GPS), a motion detecting sensor, anaccelerometer, a moisture sensor, a gyroscope, and the like. Varioussensor types that may also be used are also known in the field ofrobotics.

Examples of possible motion modules, motion-restriction modules, andmotion-guiding modules are already described above. These modules asdescribed can be based upon exertion of mechanical forces, or be basedupon electromagnetic forces, chemical forces, physical forces, using forinstance “van der Waals” forces, “Casimir forces”, based upon surfacetension, vacuum or air pressure, and the like.

Data processing unit 100 may for instance be a computer having variouscomponents known in computers, like memory, an arithmetic processor,data busses, end the like. Data processing unit 100 may be able tocontrol the other parts in the element 1. It may even control at leastpart of at least one other element. For instance, in a master-slavesetting state. It may also coordinate cooperation between elements 1. Itmay run a computer program. It may process instructions provided from anexternal source.

The various units or components in FIG. 8 are indicated schematically.The units may be incorporated in the element. In accordance withembodiments, one or more units may at least partially be integrated in aface of an element. Furthermore, In accordance with embodiments, one ormore units may at least partially be integrated into a single component.Alternatively, at least part of the functionality of the units 100-700may be incorporated in the form of a computer program product.

In FIGS. 9A-9K an embodiment of an assembly of elements 1 (labelled‘a’-′e′) comprising a shared motion module 90 is illustrated. In thedepicted embodiment, the elements do not have the same shape or size. Anadvantage of a shared motion module is that an assembly of elements canshift shape with the use of a limited number of relatively complexmotion modules 90. In FIG. 9A, element ‘a’ is provided with the sharedmotion module 90. In accordance with embodiments, shared motion module90 is temporarily assigned to element ‘a’. This may be done by a controlstructure for assigning the shared motion module, and for controllingthe shared motion module 90. Alternatively, the shared motion module 90is controlled by an element that uses the shared motion module. In yetanother embodiment, the shared motion module is self-controlled, of maybe part of a peer network together with elements, and even furthershared motion modules. The above indicated forms or modes of operationmay be combined, or the assembly of elements and one or more sharedmotion modules may switch from one mode of operation to another. Thus,processing and operation of the motion module may be operated andcontrolled from the shared motion module 90. Alternatively (and atanother end of the spectrum), operation and control of shared motionmodule 90 is done in an element 1. Operation and processing can also bedistributed. Using for instance master-slave settings, control may beswitched from element 1 to shared motion module 90 and vice versa. Also,control of a shared motion module may also be switched from one element1 to another element 1.

In the current embodiment, the shared motion module 90 comprisesattachment parts 91 that engage element ‘a’. Shared motion module 90 isin FIG. 9A in its active position. Attachment parts 91 engage element‘a’ here in such a way that shared motion module 90 cannot displace withrespect to element ‘a’. In this active position the shared motion module90 can be further activated to engage a neighbouring element to startmoving element ‘a’ with respect to such a neighbouring, in particularadjoining, element. Here, no such element is illustrated. The sharedmotion module 90 is located in a track 11, like for instance a track 11illustrated in FIG. 4A. In FIG. 9B, the attachment part 91 is pulled ininto shared motion module 90. Thus, shared motion module 90 becomes freeto move along track 11 of element ‘a’. To actually move along track 11of element ‘a’, the shared motion module 90 can be provided with adisplacement part 92. In accordance with embodiments, displacement part92 engages in the track 11 of element ‘a’. Displacement part 92 may be amechanical component, physically engaging track 11. For instance,displacement part 92 may comprise driven wheel similar for instance tothe motion module of FIGS. 4A-4L, a piezo element illustrated above in amotion module in an element and for instance similar to the embodimentsillustrated in FIGS. 6A-7D. Displacement part 92 may also comprisemagnet parts that can be activated. The track may be provided with partsthat respond to magnetic forces, but that are themselves not permanentlymagnetic, for instance iron patches. Thus, it is possible to provide amagnetic drive while the elements are themselves not permanentlymagnetic.

In FIGS. 9B-9G, it is illustrated how displacement part 92 causes sharedmotion module 90 to travel along tracks 11 of various elements (‘a’,‘c’, ‘d’) to arrive at an element 1 that is indicated ‘e’. When goingfrom FIG. 9C to 9D, the motion module follows track 11, even if thetrack 11 rounds a corner. When going from FIG. 9E to FIG. 9F, motionmodule 90 leaves element ‘a’ and continues its way in track 11 ofelement ‘d’. When going from the situation in FIG. 9F to 9G, motionmodule 90 first follows track 11 of element ‘d’, and goes to track 11 ofelement ‘e’. These tracks 11 here connect to one another and for themotion module 90 present one continuous track 11.

In FIG. 9H, it is illustrated that shared motion module 90 activates itsattachment parts 91 to engage element ‘e’. Thus, the position of theshared motion module 90 on element ‘e’ is fixed or locked throughattachment part(s) 91. Here, the attachment parts 91 are illustrated atone sided of shared motion module 90. As is evident when looking atFIGS. 9A and 9H, the attachment parts 91 can engage motion module 90from various sides. Here two sides are illustrated. In accordance withembodiments, the attachment parts 91 are designed to allow engagement ofall sides of motion module 90. Alternatively, the attachment parts 91are not incorporated in the motion module 90 itself, but may be part ofthe motion module that is integrated in an element. For instance, theattachment part 91 may be designed along the lines of the motionrestriction module shown in FIGS. 6A-6D. In fact, it may even bepossible to provide a part that is allowed to function as motionrestriction module, and as attachment part for motion module 90.

In FIG. 9H the displacement part 92 is not indicated, in order toillustrate that it is no longer functional as of this stage.

In accordance with embodiments, like for instance shown in FIG. 7A, anelement 1 comprises two crossing motion guiding modules 11, each motionguiding module 11 going around the element 1. In such an embodiment, twotypes of shared motion modules may be defined, one type of motion modulefor a first motion guiding module 11 and another for a second motionguiding module 11. These types of motion modules 90 and motion guidingmodules 11 may be identical, but oriented differently.

In FIG. 9I, it is illustrated how element displacement part 93 isactivated into its active position. The element displacement part 93extends from shared motion module 90 and from element ‘e’ into themotion guiding module, here track 11, of element t′. Again, the elementdisplacement part 93 can be similar to the types illustrated in FIGS.4A-7D, i.e., based on mechanical operation, like a wheel, a toothedgear, or the like, magnetically/activated operated elements, or forinstance piezo-type elements. The element displacement part 93 nowengages into track 11 of element ‘b’. It starts exerting force onelement ‘b’ via engagement of track 11. Consequently, element ‘d’displaces with respect to element ‘b’. FIG. 9J illustrates this. Next,In accordance with embodiments shown in FIG. 9K, the shared motionmodule 90 is stored in a storage space in an element, here element ‘d’.Thus, the tracks 11 are free, and shared motion module 90 may be in aposition to be charged, or to be protected against environmentalinfluences.

In accordance with embodiments, the displacement part 92 and elementdisplacement part 93 may functionally be combined.

In FIGS. 10A-10H, another concept of an element 1 with a motion module10 is presented schematically. In this concept, which may be combinedwith previous concepts, an element 1 has at least one motion module 10and a motion module movement part 95 allowing displacement or change oforientation of the motion module 10 in an element 1. In this way, thenumber of motion modules 10 in an element 1 can be considerably reduced.In accordance with embodiments, an element 1 comprises one motion module10 that comprises a motion module movement part 95 that allows a motionmodule to be displaced or repositioned to have an active position ateach face 3. Thus, only one motion module 10 can be sufficient ofdisplacing an element 1 with respect to another element 1. In fact, morethan one motion module 10 may be included in an element 1. In FIGS. 10Aand 10B, an embodiment of such a motion module 10 is illustrated thatcomprises a motion module movement part 95 that allows rotation of themotion module 10 inside the element 1. In that way, motion module 1 thatis at an active position at a face 3, allowing engagement of anadjoining element (not shown) that rests against the surface of face 3.In FIG. 10B, motion module 10 is rotated about rotation axis R to anactive position at the adjacent face 3 of element 1.

In FIGS. 10C-10H, an alternative embodiment for the motion module 10with an alternative motion module movement part 96 is illustrated. Inthis embodiment, motion module 10 moves parallel to motion guidingmodule 11. It is within motion guiding module 11. Motion module 10 inthis embodiment comprises a motion module movement part 96 that allowsdisplacement of motion module 10 as indicated in subsequent FIGS.10C-10G. The motion module 10 moves or displaces from its position inFIG. 10C to its position in FIG. 10D parallel to motion guiding module11, here track 11. Motion module 10 here displaces inside element 1.Here motion module 10 moves or displaces between the centre point of theelement and track 11, leaving track 11 free. The motion module may beactuated via exertion of a mechanical force. Examples are illustratedabove. Alternatively, electromagnetical force may be used. An example ofthis is also illustrated above. In this way, an element may comprise aslittle as one motion module 10, reducing complexity o an element. It mayme possible to equip an element 1 with several motion modules.

In FIG. 10F, motion module 10 is moved to come into its workingposition. In this embodiment, the motion module has a working position.In other embodiments, the motion module may be designed to move in morethan one orientation.

In FIG. 10G, motion module 10 is at its new active position at adjacentface 3. There, motion module 10 may be locked in its position in element1. In FIG. 10H, schematically, motion module 10 released an elementdisplacement part 93. In this embodiment, it may comprise a drivenwheel, like the embodiment of FIGS. 4A-4L. Other element displacementparts 93 may also be conceivable, for instance the piezo elementdescribed above, or the magnetic parts described earlier. Thisembodiment may considerably simplify elements 1, as the may comprise aslittle as one motion module 10 in an element 1. The motion module maycomprise part of the elements functional parts. In one extreme example,the motion module 10 comprises all the functional parts (FIG. 8) of theelement 1.

The embodiment of FIGS. 10A-10H may be combined with the embodiment ofFIGS. 9A-9K. For instance, an element may comprise one or moreinternally displaceable motion modules 10, in combination with one oremore shared motion modules in an object. In another embodiment, a motionmodule can be both an internal motion module, and it may function as ashared motion module 10.

It will also be clear that the above description and drawings areincluded to illustrate some embodiments of the invention, and not tolimit the scope of protection. Starting from this disclosure, many moreembodiments will be evident to a skilled person. These embodiments arewithin the scope of protection and the essence of embodiments and areobvious combinations of prior art techniques and the disclosure of thispatent.

LISTING OF REFERENCE NUMERALS

-   -   1 element    -   2 centre of an element    -   3 face of an element    -   10 motion module    -   11 motion module    -   12 slidable cover    -   14 motion guiding/motion restriction module    -   15 motion guiding/motion restriction module    -   20 motion guiding module    -   21 straight pin    -   22 groove    -   30 motion restriction module    -   31 pin    -   32 slot    -   34 cam    -   35 undercut opening in slot 3 . . .    -   70 piezo module    -   71 leg    -   72 piezo piece    -   73 piezo element    -   80 rail    -   82 undercut groove    -   90 (shared) motion module    -   91 Attachment part(s)    -   92 displacement part    -   93 element displacement part    -   95 motion module movement part    -   96 motion module movement part    -   100 data processing unit    -   200 data communication unit    -   300 energy unit    -   400 sensor unit    -   500 motion module    -   600 motion restriction unit    -   700 motion guiding module

What is claimed is:
 1. An apparatus, comprising: a three-dimensionalbody having a geometric shape and which is displaceable between aninitial state and a goal state that is different from said initialstate; a centre point in said three-dimensional body; at least one facecoupled to said centre point; a motion-restriction function to limit thedisplacement of said centre point with respect to the second centrepoint to at least one trajectory selected from a first trajectory ofsaid element and a second trajectory of another element; at least onesensor to provide input regarding the presence of anotherthree-dimensional body in contact with the at least one face; and acomputer program operationally coupled to said motion guiding function,said motion-restriction function, and said at least one sensor, saidelement computer program, when executed, is to allow displacement of thethree-dimensional body, wherein said computer program is to base atleast part of its decision-making regarding displacement of thethree-dimensional body between said initial state and said goal state ona factor of randomness.
 2. The apparatus of claim 1, further comprisinga communication module for exchanging data with at least anotherthree-dimensional body, said data including at least one positionstatus.
 3. The apparatus of claim 2, further comprising a dataprocessing module, functionally coupled to said communication module forprocessing data from said communication module.
 4. The apparatus ofclaim 3, further comprising an energy module functionally coupled tosaid motion module, said communication module, and said data processingmodule, for providing energy to at least said motion module, saidcommunication module, and said data processing module.
 5. The apparatusof claim 4, wherein said data processing module comprises softwarewhich, when executed on said data processing module, is to perform:retrieving a set position, selected from place and orientation and acombination thereof, for said three-dimensional body via said datacommunication module; retrieving current position information of saidthree-dimensional body; producing at least one motion instruction forsaid motion module for moving said three-dimensional body from saidcurrent position to said set position by moving said at least one faceover or along a face of another three-dimensional body; and providingsaid motion module with said at least one motion instruction.
 6. Theapparatus of claim 1, wherein said apparatus comprises an element for agame assembly.
 7. An element for a game assembly, comprising: a bodyhaving at least one exterior surface allowing displacement between aninitial state and a goal state that is different from said initialstate; at least one motion guiding module for displacing said body withrespect to said at least one second body over or along said at least oneexterior surface; a motion-restriction function to limit thedisplacement of said centre point with respect to the second centrepoint to at least one trajectory selected from a first trajectory ofsaid element and a second trajectory of another element a communicationmodule for exchanging data with said at least one second body; a dataprocessing module, functionally connected to said at least onemotion-restriction module, said at least one motion module, and saidcommunication module; an energy module, for providing energy to saidmotion module, said motion-restriction module, said communicationmodule, and said data processing module; and a computer programoperationally coupling said motion guiding function and saidmotion-restriction function, said element computer program, whenexecuted, is to allow displacement of the body, wherein said computerprogram is to base at least part of its decision-making regardingdisplacement of the three-dimensional body between said initial stateand said goal state on a factor of randomness.
 8. A game assembly,comprising: a plurality of elements, each element in the plurality ofelements including a three-dimensional body having a geometric shapewhich is displaceable between an initial state and a goal state that isdifferent from said initial state, a centre point in saidthree-dimensional body, at least one face coupled to said centre point,and a motion-restriction function to limit the displacement of saidcentre point with respect to the second centre point to at least onetrajectory selected from a first trajectory of said element and a secondtrajectory of another element, and at least one sensor to provide inputregarding the presence of another element in contact with said at leastone face; and an element computer program operationally coupled to saidmotion guiding function, said motion-restriction function and said atleast one sensor, and which element computer program, when executed, isto allow displacement of one or more of the elements, said elementcomputer program basing at least part of its decision-making regardingsaid displacement between the initial state and the goal state on afactor of randomness, a motion function providing one or more of theelements with independent movement ability defining a displacement ofthe centre point with respect to said second centre point of anotherelement using the motion-guiding module of that other element; and agame assembly computer program comprising instructions which, whenexecuted by the processor, is to define, in the memory, the motionfunction and a set of the elements.